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A unifying theory of a posteriori finite element error control. (English) Zbl 1100.65089

The author thoroughly states an abstract framework for a posteriori error estimation in the finite element method, based on residual formulation. He considers successively conforming, nonconforming and mixed finite element approximations applied to Laplace, Stokes and Navier-Lame model problem.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

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