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(a) Consider the differential equation -u"(x) = x in (0, 1), u(0) = u(1) = 0. (v) Taking a mesh with two elements (N = 2), compute the finite element solu- tion u,(x) for x e (0,1). Compute the error between the exact solution and the approximate solution at the node located at the midpoint of the interval lu,(0.5)- u(0.5). %3D

(a) Consider the differential equation -u"(x) = x in (0, 1), u(0) = u(1) = 0. (v) Taking a mesh with two elements (N = 2), compute the finite element solu- tion u,(x) for x e (0,1). Compute the error between the exact solution and the approximate solution at the node located at the midpoint of the interval lu,(0.5)- u(0.5). %3D

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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(a) Consider the differential equation -u"(x) = x in (0, 1), u(0) = u(1) = 0. %3D (v) Taking a mesh with two elements (N = 2), compute the finite element solu- tion u,(x) for x e (0, 1). Compute the error between the exact solution and the approximate solution at the node located at the midpoint of the interval lu,(0.5) – u(0.5)). %3D
Transcribed Image Text:(a) Consider the differential equation -u"(x) = x in (0, 1), u(0) = u(1) = 0. %3D (v) Taking a mesh with two elements (N = 2), compute the finite element solu- tion u,(x) for x e (0, 1). Compute the error between the exact solution and the approximate solution at the node located at the midpoint of the interval lu,(0.5) – u(0.5)). %3D
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