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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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An adaptive strategy for elliptic problems including a posteriori controlled boundary approximation
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by W. Dörfler and M. Rumpf PDF
Math. Comp. 67 (1998), 1361-1382 Request permission


We derive a posteriori error estimates for the approximation of linear elliptic problems on domains with piecewise smooth boundary. The numerical solution is assumed to be defined on a Finite Element mesh, whose boundary vertices are located on the boundary of the continuous problem. No assumption is made on a geometrically fitting shape. A posteriori error estimates are given in the energy norm and the $L^2$-norm, and efficiency of the adaptive algorithm is proved in the case of a saturated boundary approximation. Furthermore, a strategy is presented to compute the effect of the non-discretized part of the domain on the error starting from a coarse mesh. This especially implies that parts of the domain, where the measured error is small, stay non-discretized. The presented algorithm includes a stable path following to supply a sufficient polygonal approximation of the boundary, the reliable computation of the a posteriori estimates and a mesh adaptation based on Delaunay techniques. Numerical examples illustrate that errors outside the initial discretization will be detected.
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Additional Information
  • W. Dörfler
  • Affiliation: Institut für Angewandte Mathematik, Universität Freiburg, Hermann-Herder- Strasse 10, D-79104 Freiburg, Germany
  • Email:
  • M. Rumpf
  • Affiliation: Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse 6, D-52115 Bonn, Germany
  • MR Author ID: 604100
  • Email:
  • Received by editor(s): March 4, 1996
  • Received by editor(s) in revised form: January 23, 1997
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 1361-1382
  • MSC (1991): Primary 65N15, 65N30, 65N50
  • DOI:
  • MathSciNet review: 1489969