We will discuss this issue in chapter 2 0 22

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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 N 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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