Stopping Criteria Based on Locally Reconstructed Fluxes
We propose stopping criteria for the iterative solution of equations resulting from discretization by conforming, nonconforming, and total discontinuous finite element methods. A simple modification of error estimators based on locally reconstructed fluxes allows to split the estimator into a discretisation-based and an iteration-based part. Comparison of both then leads to stopping criteria which can be used in the framework of an adaptive algorithm.
KeywordsPosteriori Error Adaptive Mesh Multigrid Method Posteriori Error Estimate Iterative Solver
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- 2.R. Becker, D. Capatina, R. Luce, Robust local flux reconstruction for various finite element methods, in Numerical Mathematics and Advanced Applications: Proceedings of ENUMATH’ 2013, Lausanne, ed. by A. Abdulle et al. (2014), pp. 65–73. doi:10.1007/978-3-319-10705-9_6Google Scholar
- 6.W. Hackbusch, Multigrid Methods and Applications. Springer Series in Computational Mathematics, vol. 4 (Springer, Berlin, 1985)Google Scholar
- 10.P.-A. Raviart, J.-M. Thomas, A mixed finite element method for 2nd order elliptic problems, in Mathematical Aspects of Finite Element Methods: Proceedings of the Conference Consiglio Naz. delle Ricerche, Rome (Springer, Berlin, 1977), pp. 292–315Google Scholar