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The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 00 on 0

The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 00 on 0

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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DISCUSSION Before posting to the discussion board, complete the following: The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 0<x<1, c(x) >0 on 0<x<1 -u"(x)+c(x)u(x)=f(x), u(0)=0, u(1)=0 The weak form of this BVP was given as where a(u, v) = f(v), for all v EV a(u, v) = f'(u'v' + cuv)dx, for all u,veV, (v)=f(x)v(x) dx, for all ve V Post a response to the following discussion questions. What value does the weak formulation offer? What is the possible shortcoming of the weak formulation? Does one arrive at a minimization problem by substituting v=du, the variation in u, ; i.e.. can one arrive at an integral such that yields the original equation? 1 V = [ f(u,u',x) dx v 0
Transcribed Image Text:DISCUSSION Before posting to the discussion board, complete the following: The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 0<x<1, c(x) >0 on 0<x<1 -u"(x)+c(x)u(x)=f(x), u(0)=0, u(1)=0 The weak form of this BVP was given as where a(u, v) = f(v), for all v EV a(u, v) = f'(u'v' + cuv)dx, for all u,veV, (v)=f(x)v(x) dx, for all ve V Post a response to the following discussion questions. What value does the weak formulation offer? What is the possible shortcoming of the weak formulation? Does one arrive at a minimization problem by substituting v=du, the variation in u, ; i.e.. can one arrive at an integral such that yields the original equation? 1 V = [ f(u,u',x) dx v 0
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