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A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization. (English) Zbl 1142.65086

Summary: We present in this Note fully computable a posteriori error estimates allowing for accurate error control in the conforming finite element discretization of pure diffusion problems. The derived estimates are based on the local conservativity of the conforming finite element method on a dual grid associated with simplex vertices rather than directly on the Galerkin orthogonality.

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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