An adaptive finite element method for linear elliptic problems

Authors:
Kenneth Eriksson and Claes Johnson

Journal:
Math. Comp. **50** (1988), 361-383

MSC:
Primary 65N30; Secondary 65N50

DOI:
https://doi.org/10.1090/S0025-5718-1988-0929542-X

MathSciNet review:
929542

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Abstract: We propose an adaptive finite element method for linear elliptic problems based on an optimal maximum norm error estimate. The algorithm produces a sequence of successively refined meshes with a final mesh on which a given error tolerance is satisfied. In each step the refinement to be made is determined by locally estimating the size of certain derivatives of the exact solution through computed finite element solutions. We analyze and justify the algorithm in a model case.

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0929542-X

Article copyright:
© Copyright 1988
American Mathematical Society