This article is cited in 4 papers

Mesh adaptation based on functional a posteriori estimates with Raviart–Thomas approximation

M. E. Frolov, M. A. Churilova

Saint-Petersburg State Polytechnical University

Abstract: Adaptive algorithms based on functional a posteriori estimates for the Dirichlet problem for the stationary diffusion equation with jump discontinuities in the equation coefficients are compared. The algorithms have been implemented in MATLAB with the use of both standard finite element approximations and the zero-order Raviart–Thomas approximation. The adaptation results are analyzed using indicators of the local error distribution. Specifically, sequences of finite-element partitions, effectivity indices of estimates, and relative errors of approximate solutions are compared.

Key words: functional a posteriori estimates, stationary diffusion equation, adaptive algorithms, Raviart–Thomas approximation.

UDC: 519.63

Received: 18.11.2011
Revised: 26.01.2012

 English version: Computational Mathematics and Mathematical Physics, 2012, 52:7, 1044–1054

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