Problem 1 [4 marks] Let a(,) be a bilinear form on H2(2) x H²(N) and L(-) is a linear functional on H2(2) such that there exist a unique finite element solution u, E Vh satisfying a(uh, v) = L(v) Vv E Vh. Suppose {oi}1 C Vh are the basis functions of Vh: Show that a(uh, v) = L(v) Vv e Vh if and only if a(u, 6;) = L(ø;) V j = 1,2.., N. %3D
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