(Linear elements on intervals) In one dimension the
Chapter 8, Problem 3(choose chapter or problem)
(Linear elements on intervals) In one dimension the geometric building blocksoftheniteelementmethodaretheintervals.Letthetrialfunction vj(x) be the tent function dened by vj(x)=1 j +x for j 1 x j,vj(x)=1+ j x for j x j +1, and vj(x)=0 elsewhere.That is, vj(x) is continuous and piecewise-linear with vj(j)=1 and vj(k)=0 for all integers k = j. (a) Show that[vj(x)]2dx=2 and vj (x)vj+1(x)dx=1. (b) Deduce that the one-dimensional analog of the matrix mij is the tridiagonal matrix with 2 along the diagonal and 1 next to the diagonal.
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