Abstract
Usually, error estimators for adaptive refinement require exact discrete solutions. In this paper, we show how inaccurate solutions (e.g., iterative approximations) can be used, too. As a side remark we characterise iterative solution schemes that are particularly suited to producing good approximations for error estimators.
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References
Babuška, I., Miller, A.: A feedback finite element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimator. Comput. Methods Appl. Mech. Eng.61, 1–40 (1987).
Becker, R., Johnson, C., Rannacher, R.: Adaptive error control for multigrid finite element methods. Computing55, 271–288 (1995).
Dörfler, W., Rumpf, M.: An adaptive strategy for elliptic problems including a posteriori controlled boundary approximation. Math. Comp. (to appear)
Hackbusch, W.: Multi-grid methods and applications. Berlin, Heidelberg, New York: Springer 1985.
Hackbusch, W.: Iterative solution of large sparse systems of equations. Berlin, Heidelberg, New York, Tokyo: Springer 1994.
Verfürth, R.: A review of a posteriori error estimation and adaptive mesh-refinement techniques. Stuttgart: Teubner 1996.
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This work was supported by Deutsche Forschungsgemeinschaft (Project Ha 1324/9).
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Hackbusch, W., Wappler, J.U. Remarks on a posteriori error estimation for inaccurate finite element solutions. Computing 60, 175–191 (1998). https://doi.org/10.1007/BF02684364
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DOI: https://doi.org/10.1007/BF02684364