A posteriori error analysis for locally conservative mixed methods
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Abstract:
In this work we present a theoretical analysis for a residual-type error estimator for locally conservative mixed methods. This estimator was first introduced by Braess and Verfürth for the Raviart–Thomas mixed finite element method working in mesh-dependent norms. We improve and extend their results to cover any locally conservative mixed method under minimal assumptions, in particular, avoiding the saturation assumption made by Braess and Verfürth. Our analysis also takes into account discontinuous coefficients with possibly large jumps across interelement boundaries. The main results are applied to the $P1$ nonconforming finite element method and the interior penalty discontinuous Galerkin method as well as the mixed finite element method.References
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Additional Information
- Kwang Y. Kim
- Affiliation: Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea 305–701
- Email: toheart@acoustic.kaist.ac.kr
- Received by editor(s): January 16, 2005
- Received by editor(s) in revised form: September 27, 2005
- Published electronically: October 4, 2006
- Additional Notes: This work was supported by the Brain Korea 21 project, Korea.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 76 (2007), 43-66
- MSC (2000): Primary 65N30; Secondary 65N15
- DOI: https://doi.org/10.1090/S0025-5718-06-01903-X
- MathSciNet review: 2261011