Total Flux Estimates for a Finite-Element Approximation of Elliptic Equations |
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Authors: | BARRETT JOHN W; ELLIOTT CHARLES M |
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Institution: |
Department of Mathematics, Imperial College London SW7 2BZ
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Abstract: | An elliptic boundary-value problem on a domain with prescribedDirichlet data on I is approximated using a finite-elementspace of approximation power hK in the L2 norm. It is shownthat the total flux across I can be approximated with an errorof O(hK) when is a curved domain in Rn (n = 2 or 3) and isoparametricelements are used. When is a polyhedron, an O(h2K2)approximation is given. We use these results to study the finite-elementapproximation of elliptic equations when the prescribed boundarydata on I is the total flux.
Present address: School of Mathematical and Physical Sciences,University of Sussex, Brighton, Sussex BN1 9QH. |
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