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2013 | OriginalPaper | Chapter

An Adaptive MFD Method for the Obstacle Problem

Authors : P. F. Antonietti, L. Beirão da Veiga, M. Verani

Published in: Numerical Mathematics and Advanced Applications 2011

Publisher: Springer Berlin Heidelberg

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Abstract

We present an adaptive mimetic finite difference method for the approximate solution of variational inequalities. The adaptive strategy is based on a heuristic hierarchical type error indicator. Numerical experiments that validate the performance of the adaptive MFD method are also presented.

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Literature
1.
go back to reference M. Ainsworth and J. T. Oden. A posteriori error estimation in finite element analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2000. M. Ainsworth and J. T. Oden. A posteriori error estimation in finite element analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2000.
2.
go back to reference P. F. Antonietti, L. Beirão da Veiga, and M. Verani. A mimetic discretization of elliptic obstacle problems. To appear on Math. Comp. P. F. Antonietti, L. Beirão da Veiga, and M. Verani. A mimetic discretization of elliptic obstacle problems. To appear on Math. Comp.
3.
go back to reference P. F. Antonietti, L. Beirão da Veiga, C. Lovadina and M. Verani. Hierarchical a posteriori error estimators for the mimetic discretization of elliptic problems. Technical Report 33, MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy, 2010. http://mox.polimi.it/it/progetti/pubblicazioni/. P. F. Antonietti, L. Beirão da Veiga, C. Lovadina and M. Verani. Hierarchical a posteriori error estimators for the mimetic discretization of elliptic problems. Technical Report 33, MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy, 2010. http://​mox.​polimi.​it/​it/​progetti/​pubblicazioni/​.
5.
go back to reference F. A. Bornemann, B. Erdmann, and R. Kornhuber. A posteriori error estimates for elliptic problems in two and three space dimensions. SIAM J. Numer. Anal., 33(3):1188–1204, 1996.MathSciNetMATHCrossRef F. A. Bornemann, B. Erdmann, and R. Kornhuber. A posteriori error estimates for elliptic problems in two and three space dimensions. SIAM J. Numer. Anal., 33(3):1188–1204, 1996.MathSciNetMATHCrossRef
6.
go back to reference H. Brezis and G. Stampacchia. Sur la régularité de la solution d’inéquations elliptiques. Bull. Soc. Math. France, 96:153–180, 1968.MathSciNetMATH H. Brezis and G. Stampacchia. Sur la régularité de la solution d’inéquations elliptiques. Bull. Soc. Math. France, 96:153–180, 1968.MathSciNetMATH
7.
go back to reference F. Brezzi, A. Buffa, and K. Lipnikov. Mimetic finite differences for elliptic problems. M2AN Math. Model. Numer. Anal., 43(2):277–295, 2009. F. Brezzi, A. Buffa, and K. Lipnikov. Mimetic finite differences for elliptic problems. M2AN Math. Model. Numer. Anal., 43(2):277–295, 2009.
8.
go back to reference P. G. Ciarlet, The finite element method for elliptic problems, North-Holland, Amsterdam, 1978.MATH P. G. Ciarlet, The finite element method for elliptic problems, North-Holland, Amsterdam, 1978.MATH
9.
go back to reference R. H. Nochetto, K. G. Siebert, and A. Veeser, Pointwise a posteriori error control for elliptic obstacle problems. Numer. Math., 95(1):163–195, 2003MathSciNetMATHCrossRef R. H. Nochetto, K. G. Siebert, and A. Veeser, Pointwise a posteriori error control for elliptic obstacle problems. Numer. Math., 95(1):163–195, 2003MathSciNetMATHCrossRef
10.
go back to reference Q. Zou, A. Veeser, R. Kornhuber, C. Graser Hierarchical error estimates for the energy functional in obstacle problems. Numer. Math., 117(4):653–677, 2011.MathSciNetMATHCrossRef Q. Zou, A. Veeser, R. Kornhuber, C. Graser Hierarchical error estimates for the energy functional in obstacle problems. Numer. Math., 117(4):653–677, 2011.MathSciNetMATHCrossRef
Metadata
Title
An Adaptive MFD Method for the Obstacle Problem
Authors
P. F. Antonietti
L. Beirão da Veiga
M. Verani
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-33134-3_1

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