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A posteriori error analysis for locally conservative mixed methods. (English) Zbl 1121.65112
This paper improves and extends the theoretical analysis for a residual-type error estimator for locally conservative mixed methods developed by D. Braess and R. Verfürth [SIAM J. Numer. Anal. 33, No. 6, 2431–2444 (1996; Zbl 0866.65071)] for the Raviart-Thomas mixed finite element method working in mesh-dependent norms. These new results cover any locally conservative mixed method under minimal assumptions. In particular, they avoid the saturation assumption made by Braess and Verfürth [loc. cit.] and they also take into account discontinuous coefficients with possibly large jumps across interelement boundaries. These mathematical results are completed by convincing numerical experiments.

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