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Unformatted text preview: to the exact solution.
0 1 4. The Galerkin form of (1.3.1) consists of determining u 2 H01 such that (1.3.2) is
satis ed. Similarly, the nite element solution U 2 S0
H01 satis es (1.2.12).
Letting e(x) = u(x) ; U (x), show A(e e) = A(u u) ; A(U U )
where the strain energy A(v u) is given by (1.3.2c). We have, thus, shown that the
strain energy of the error is the error of the strain energy. Bibliography
1] I. Babuska, J. Chandra, and J.E. Flaherty, editors. Adaptive Computational Methods
for Partial Di erential Equations, Philadelphia, 1983. SIAM.
2] I. Babuska, O.C. Zienkiewicz, J. Gago, and E.R. de A. Oliveira, editors. Accuracy
Estimates and Adaptive Re nements in Finite Element Computations. John Wiley
and Sons, Chichester, 1986.
3] M.W. Bern, J.E. Flaherty, and M. Luskin, editors. Grid Generation and Adaptive
Algorithms, volume 113 of The IMA Volumes in Mathematics and its Applications,
New York, 1999. Springer.
4] G.F. Carey. Computational Grids: Generation, Adaptation, and Solutio...
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- Spring '14