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A posteriori error analysis for locally conservative mixed methods


Author: Kwang Y. Kim
Journal: Math. Comp. 76 (2007), 43-66
MSC (2000): Primary 65N30; Secondary 65N15
DOI: https://doi.org/10.1090/S0025-5718-06-01903-X
Published electronically: October 4, 2006
MathSciNet review: 2261011
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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.


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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

DOI: https://doi.org/10.1090/S0025-5718-06-01903-X
Keywords: a posteriori error analysis, locally conservative mixed methods, mixed finite element methods, nonconforming finite element methods, discontinuous Galerkin methods
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.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.