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Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems.
- Source :
- Numerische Mathematik; Sep2010, Vol. 116 Issue 3, p383-419, 37p, 4 Diagrams, 3 Charts, 3 Graphs
- Publication Year :
- 2010
-
Abstract
- Recently an adaptive nonconforming finite element method (ANFEM) has been developed by Carstensen and Hoppe (in Numer Math 103:251–266, 2006). In this paper, we extend the result to some nonsymmetric and indefinite problems. The main tools in our analysis are a posteriori error estimators and a quasi-orthogonality property. In this case, we need to overcome two main difficulties: one stems from the nonconformity of the finite element space, the other is how to handle the effect of a nonsymmetric and indefinite bilinear form. An appropriate adaptive nonconforming finite element method featuring a marking strategy based on the comparison of the a posteriori error estimator and a volume term is proposed for the lowest order Crouzeix–Raviart element. It is shown that the ANFEM is a contraction for the sum of the energy error and a scaled volume term between two consecutive adaptive loops. Moreover, quasi-optimality in the sense of quasi-optimal algorithmic complexity can be shown for the ANFEM. The results of numerical experiments confirm the theoretical findings. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0029599X
- Volume :
- 116
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Numerische Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 53362006
- Full Text :
- https://doi.org/10.1007/s00211-010-0307-6