# Triangulation No of elements = 16 No of nodes = 13 No interior nodes = 5 No of boundary nodes = 8

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### Text of Triangulation No of elements = 16 No of nodes = 13 No interior nodes = 5 No of boundary nodes = 8

• Slide 1
• Triangulation No of elements = 16 No of nodes = 13 No interior nodes = 5 No of boundary nodes = 8
• Slide 2
• With the triangulation we associate the function space consisting of continuous, piecewise linear functions on vanishing on i.e Triangulation No interior nodes = 5 No of global basis functions = 5
• Slide 3
• 1 2 3 4 5 6 7 8 9 10 11 12 13 Element Labeling 14 15 16
• Slide 4
• Node Labeling (global labeling) 12 34 5 6 7 8 9 1011 1213
• Slide 5
• global basis functions 12 34 5 6 7 8 9 1011 1213
• Slide 6
• 12 34 5 6 7 8 9 1011 1213 global basis functions
• Slide 7
• Global basis functions
• Slide 8
• global basis functions 12 34 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 0 1011 5 1312
• Slide 9
• 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
• Slide 10
• global basis functions 12 34 6 7 8 9 0 0 0 0 0 0 0 0 1011 5 1312 0 0
• Slide 11
• 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 12 34 5 6 7 8 9 1011 1213 Assemble linear system
• Slide 12
• 12 34 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 0 1011 5 1312 12 34 6 7 8 9 0 0 0 0 0 0 0 0 1011 5 1312 0 0
• Slide 13
• Approximation of u 01 02 03 04 0.0695 06 07 08 09 0.04910 0.04911 0.04912 0.04913
• Slide 14
• Node Label (local labeling) 12 3 Each triangle has 3 nodes. Label them locally inside the triangle
• Slide 15
• Node and Element Label
• Slide 16
• Local label.vs. global label Matrix t(3,#elements) 16151413121110987654321 131211105555432132141 1211101312111013 12111087692 8769131211108769121110133
• Slide 17
• X-coordinate and y-coordinate Matrix p(2,#elements) 13121110987654321 0.750.25 0.7510.50 1001x 0.25 0.75 0.50 1 0011y
• Slide 18
• Boundary node vector e(#boundary node) e8e7e6e5e4e3e2e1 98764321start 14329876end
• Slide 19
• Approximation of u 01 02 03 04 0.0695 06 07 08 09 0.04910 0.04911 0.04912 0.04913
• Slide 20
• Global basis functions
• Slide 21
• Triangulation

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