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A posteriori error estimators for the Raviart-Thomas element. (English) Zbl 0866.65071

This paper is concerned with the development of a posteriori error estimators for the Raviart-Thomas element which is really powerful for mixed finite element methods. The difficulties met in such a development are:
– the \(H(\text{div},\Omega)\)-norm is an anisotropic norm since it refers to differential operators of different orders;
– the traces of \(H(\text{div},\Omega)\)-functions are only in \(H^{-1/2}\).
The authors obtain and analyze reliable and efficient residual error estimators for the error measured in mesh-dependent norms.
This paper includes all the proofs and is nicely written.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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