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Functional-type a posteriori error estimates for mixed finite element methods. (English) Zbl 1086.65103

This paper concerns a posteriori error estimation for the primal and dual mixed finite element methods applied to the diffusion problem, considered in a general setting with inhomogeneous mixed Dirichlet-Neumann boundary conditions. New functional-type a posteriori error estimators are proposed that exhibit the ability both to indicate local error distribution and to ensure upper bounds for discretization errors in primal and dual (flux) variables. The estimators are computationally cheap and require only the projections of piecewise constant functions on to the spaces of lowest-order Raviart-Thomas or continuous piecewise linear elements. It is shown how these projections can easily be realized by simple local averaging.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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