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A posteriori error estimates for mixed finite element approximations of elliptic problems. (English) Zbl 1136.65101
The authors derive residual based a posteriori error estimates of the flux in \(L^{2}\)-norm for a general class of mixed methods for elliptic problems. The estimate is applicable to standard mixed methods such as the Raviart-Thomas-Nedelec and Brezzi-Douglas-Marini elements, as well as stabilized methods such as the Galerkin-least squares method. The element residual in the estimation employs an elementwise computable postprocessed approximation of the displacement which gives optimal order.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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