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A posteriori error estimate for the mixed finite element method. (English) Zbl 0864.65068
Summary: A computable error bound for mixed finite element methods is established in the model case of the Poisson problem to control the error in the \(H (\text{div}, \Omega) \times L^2 (\Omega)\)-norm. The reliable and efficient a posteriori error estimate applies, e.g., to Raviart-Thomas, Brezzi-Douglas-Marini, and Brezzi-Douglas-Fortin-Marini elements.

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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