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

Authors:
Francesca Fierro;Andreas Veeser
Affiliations:
Dipartimento di Matematica, Università Degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy;Institut für Angewandte Mathematik, Albert-Luwigs-Universität Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg I. Br., Germany
Venue:
Mathematics of Computation
Year:
2003

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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.