A posteriori error analysis for locally conservative mixed methods

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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 Verfurth 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 Verfurth. 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.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2006
Language
English
Article Type
Article
Keywords

FINITE-ELEMENT METHODS; ELLIPTIC PROBLEMS; QUADRILATERAL GRIDS; VOLUME METHODS; ESTIMATORS; DISCRETIZATIONS; APPROXIMATION; COEFFICIENTS

Citation

MATHEMATICS OF COMPUTATION, v.76, no.257, pp.43 - 66

ISSN
0025-5718
URI
http://hdl.handle.net/10203/86497
Appears in Collection
RIMS Journal Papers
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