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A unifying theory of a posteriori error control for nonconforming finite element methods. (English) Zbl 1127.65083
Residual-based a posteriori error estimates for nonconforming elements contain extra terms in comparison to the conforming case, e.g., jumps of tangential components. A unified framework is the topic. The paper starts with mixed methods and assumes that there is an associated space $$V_h^{nc}$$ of nonconforming elements. Another hypothesis is the existence of a space $$V_h^c$$ of conforming elements for which an interpolation operator of Clément type and a mapping $$V_h^c\to V_h^{nc}$$ exist. Three tables contain lists of examples to which the theory applies. The efficiency of the estimators is not treated in this general framework.

##### 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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