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

Fierro, Francesca; Veeser, Andreas

doi:10.1090/S0025-5718-03-01507-2

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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
Posted: 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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