Numerical Solutions of PDE by the FEM

Embed Size (px)

Citation preview

  • 7/30/2019 Numerical Solutions of PDE by the FEM

    1/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    2/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    3/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    4/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    5/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    6/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    7/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    8/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    9/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    10/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    11/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    12/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    13/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    14/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    15/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    16/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    17/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    18/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    19/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    20/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    21/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    22/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    23/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    24/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    25/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    26/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    27/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    28/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    29/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    30/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    31/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    32/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    33/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    34/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    35/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    36/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    37/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    38/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    39/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    40/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    41/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    42/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    43/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    44/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    45/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    46/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    47/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    48/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    49/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    50/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    51/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    52/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    53/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    54/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    55/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    56/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    57/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    58/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    59/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    60/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    61/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    62/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    63/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    64/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    65/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    66/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    67/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    68/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    69/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    70/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    71/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    72/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    73/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    74/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    75/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    76/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    77/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    78/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    79/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    80/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    81/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    82/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    83/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    84/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    85/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    86/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    87/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    88/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    89/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    90/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    91/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    92/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    93/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    94/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    95/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    96/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    97/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    98/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    99/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    100/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    101/142

  • 7/30/2019 Numerical Solutions of PDE by the FEM

    102/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    103/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    104/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    105/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    106/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    107/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    108/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    109/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    110/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    111/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    112/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    113/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    114/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    115/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    116/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    117/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    118/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    119/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    120/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    121/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    122/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    123/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    124/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    125/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    126/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    127/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    128/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    129/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    130/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    131/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    132/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    133/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    134/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    135/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    136/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    137/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    138/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    139/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    140/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    141/142PDF created with pdfFactory Pro trial version www.pdffactory.com

    http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/
  • 7/30/2019 Numerical Solutions of PDE by the FEM

    142/142