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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 2024 MCQ for Mathematics of Computation is 1.78.

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On the a posteriori error analysis for equations of prescribed mean curvature
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by Francesca Fierro and Andreas Veeser;
Math. Comp. 72 (2003), 1611-1634
DOI: https://doi.org/10.1090/S0025-5718-03-01507-2
Published electronically: March 26, 2003

Abstract:

We present two approaches to the a posteriori error analysis for prescribed mean curvature equations. The main difference between them concerns the estimation of the residual: without or with computable weights. In the second case, the weights are related to the eigenvalues of the underlying operator and thus provide local and computable information about the conditioning. We analyze the two approaches from a theoretical viewpoint. Moreover, we investigate and compare the performance of the derived indicators in an adaptive procedure. Our theoretical and practical results show that it is advantageous to estimate the residual in a weighted way.
References
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Bibliographic Information
  • Francesca Fierro
  • Affiliation: Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy
  • Email: fierro@mat.unimi.it
  • Andreas Veeser
  • Affiliation: Institut für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg i. Br., Germany
  • Email: andy@mathematik.uni-freiburg.de
  • Received by editor(s): September 19, 2001
  • Received by editor(s) in revised form: March 27, 2002
  • Published electronically: March 26, 2003
  • Additional Notes: Research partially supported by the TMR network “Viscosity Solutions and Their Applications”, the CNR Contract CU99.01713.CT01, and Italian M.I.U.R. Cofin2000 Project “Calcolo Scientifico: Modelli e Metodi Numerici Innovativi”.
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 72 (2003), 1611-1634
  • MSC (2000): Primary 65N30, 65N15; Secondary 35J25
  • DOI: https://doi.org/10.1090/S0025-5718-03-01507-2
  • MathSciNet review: 1986796