A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements

Wohlmuth, Barbara; Hoppe, Ronald

doi:10.1090/S0025-5718-99-01125-4

A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements
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by Barbara I. Wohlmuth and Ronald H. W. Hoppe PDF

Math. Comp. 68 (1999), 1347-1378 Request permission

Abstract:

We consider mixed finite element discretizations of linear second order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangulations. In particular, we present and analyze four different kinds of error estimators: a residual based estimator, a hierarchical one, error estimators relying on the solution of local subproblems and on a superconvergence result, respectively. Finally, we examine the relationship between the presented error estimators and compare their local components.

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