Error control and adaptivity for a variational model problem defined on functions of bounded variation

Bartels, Sören

doi:10.1090/S0025-5718-2014-02893-7

Error control and adaptivity for a variational model problem defined on functions of bounded variation
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by Sören Bartels;

Math. Comp. 84 (2015), 1217-1240

DOI: https://doi.org/10.1090/S0025-5718-2014-02893-7

Published electronically: October 23, 2014

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Abstract:

We derive a fully computable, optimal a posteriori error estimate for the finite element approximation of a total variation regularized model problem and devise an adaptive refinement strategy. Numerical experiments reveal a significant improvement over related approximations on uniformly refined triangulations.

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