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On the a posteriori error analysis for equations of prescribed mean curvature

Authors: Francesca Fierro and Andreas Veeser
Journal: Math. Comp. 72 (2003), 1611-1634
MSC (2000): Primary 65N30, 65N15; Secondary 35J25
Published electronically: March 26, 2003
MathSciNet review: 1986796
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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.

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Additional Information

Francesca Fierro
Affiliation: Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy

Andreas Veeser
Affiliation: Institut für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg i. Br., Germany

Keywords: A~posteriori error estimates, adaptive finite element methods, prescribed mean curvature equations, nonparametric minimal surfaces
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”.
Article copyright: © Copyright 2003 American Mathematical Society