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me180_hw03 - HOMEWORK 3 ERROR ESTIMATION AND ADAPTIVE...

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HOMEWORK 3: ERROR ESTIMATION AND ADAPTIVE MESHING Consider the boundary value problem d dx A 1 du dx = f ( x ), A 1 = 1, with domain Ω = (0 , L ), L = 1, and solution u ( x ) = cos(19 πx 4 ). Compute the finite element solution u N to this problem using linear equal-sized elements. Determine how many elements are needed in order to achieve e N def = || u - u N || A 1 (Ω) || u || A 1 (Ω) TOL = 0 . 05 , || u || A 1 (Ω) def = s Z Ω du dx A 1 du dx dx Plot I versus E I , where E 2 I def = 1 h I || u - u N || 2 A 1 I ) 1 L || u || 2 A 1 (Ω) . Here I is the element index, h I is the length of element I , and || u || 2 A 1 I ) def = Z Ω I du dx A 1 du dx dx . Modify your code from HW 1 so that it can automatically refine the mesh the following criterion:
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