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
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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![Problem 1 [4 marks] Let a(, ) be a bilinear form on H2(2) x H2(2) 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 Vn. 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(uh, 0;) = L(%;) V j = 1,2..., N.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61171a95-4a26-4074-aaac-1d4b8f5b0e22%2F56d01ed2-2a81-45df-84b3-a2f35b0fff07%2F7qefozd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1 [4 marks] Let a(, ) be a bilinear form on H2(2) x H2(2) 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 Vn. 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(uh, 0;) = L(%;) V j = 1,2..., N.
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