Error estimates for a finite element solution of the diffusion equation based on composite norms

A. Agouzal; K. Lipnikov; Yu. Vassilevski

doi:10.1515/JNUM.2009.006

Published by De Gruyter July 24, 2009

Error estimates for a finite element solution of the diffusion equation based on composite norms

A. Agouzal , K. Lipnikov and Yu. Vassilevski

From the journal Journal of Numerical Mathematics

https://doi.org/10.1515/JNUM.2009.006

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Abstract

We develop new a posteriori error estimates for the P₁ finite element approximation of the diffusion equation with an arbitrary piecewise constant tensor K. The estimates are established for a special composite norm of the error that is formed by the energy norm of the solution error and the K^–1/2-weighted L₂-norm of the flux error.

Keywords:: finite elements; anisotropic meshes; a posteriori error estimates

^‡Corresponding author, Institute of Numerical Mathematics, Russ. Acad. Sci., Moscow 119333, Russia, vasilevs@dodo.inm.ras.ru.

Received: 2008-06-17

Revised: 2009-04-14

Published Online: 2009-07-24

Published in Print: 2009-July

Error estimates for a finite element solution of the diffusion equation based on composite norms

Abstract

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