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-((1+x)u') = 0, x = 1 = [0,1], u(0) = 0, u'(1) = 1 Divide the interval I into three subintervals of equal length h =1/3 and let V be the corresponding space of continuous piecewise linear functions vanishing at x = 0,1. Find the variational form and finite element method Verify that the stiffness matrix A is given by: [16 -9 0 1 A = 33 -9 20 -11 2 0 -11 11 +3 3 J Q5: Consider the semi discrete finite element solution is (u(t), v) + a(u(t), v) = (f(t), v) € Let a(u(t), v) be v-elliptic and continues bilinear form, prove that the stability estimate satisfies ||u(T)||ea||u(0)| +Se e-a(T-t) ||fl| dt Q6: Given the triangulation of figure, determine the basis function and compute the integrals : 3 (0,1) dx, 243dx, 41 42 dx, 414fdx. 1. V2 dx. น 2 (0,0) (1,0)

-((1+x)u') = 0, x = 1 = [0,1], u(0) = 0, u'(1) = 1 Divide the interval I into three subintervals of equal length h =1/3 and let V be the corresponding space of continuous piecewise linear functions vanishing at x = 0,1. Find the variational form and finite element method Verify that the stiffness matrix A is given by: [16 -9 0 1 A = 33 -9 20 -11 2 0 -11 11 +3 3 J Q5: Consider the semi discrete finite element solution is (u(t), v) + a(u(t), v) = (f(t), v) € Let a(u(t), v) be v-elliptic and continues bilinear form, prove that the stability estimate satisfies ||u(T)||ea||u(0)| +Se e-a(T-t) ||fl| dt Q6: Given the triangulation of figure, determine the basis function and compute the integrals : 3 (0,1) dx, 243dx, 41 42 dx, 414fdx. 1. V2 dx. น 2 (0,0) (1,0)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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-((1+x)u') = 0, x = 1 = [0,1], u(0) = 0, u'(1) = 1 Divide the interval I into three subintervals of equal length h =1/3 and let V be the corresponding space of continuous piecewise linear functions vanishing at x = 0,1. Find the variational form and finite element method Verify that the stiffness matrix A is given by: [16 -9 0 1 A = 33 -9 20 -11 2 0 -11 11 +3 3 J Q5: Consider the semi discrete finite element solution is (u(t), v) + a(u(t), v) = (f(t), v) € Let a(u(t), v) be v-elliptic and continues bilinear form, prove that the stability estimate satisfies ||u(T)||ea||u(0)| +Se e-a(T-t) ||fl| dt Q6: Given the triangulation of figure, determine the basis function and compute the integrals : 3 (0,1) dx, 243dx, 41 42 dx, 414fdx. 1. V2 dx. น 2 (0,0) (1,0)
Transcribed Image Text:-((1+x)u') = 0, x = 1 = [0,1], u(0) = 0, u'(1) = 1 Divide the interval I into three subintervals of equal length h =1/3 and let V be the corresponding space of continuous piecewise linear functions vanishing at x = 0,1. Find the variational form and finite element method Verify that the stiffness matrix A is given by: [16 -9 0 1 A = 33 -9 20 -11 2 0 -11 11 +3 3 J Q5: Consider the semi discrete finite element solution is (u(t), v) + a(u(t), v) = (f(t), v) € Let a(u(t), v) be v-elliptic and continues bilinear form, prove that the stability estimate satisfies ||u(T)||ea||u(0)| +Se e-a(T-t) ||fl| dt Q6: Given the triangulation of figure, determine the basis function and compute the integrals : 3 (0,1) dx, 243dx, 41 42 dx, 414fdx. 1. V2 dx. น 2 (0,0) (1,0)
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