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Quasi-interpolation and a posteriori error analysis in finite element methods. (English) Zbl 0948.65113
A quasi-interpolation operator, modified in the setting of a partition of unity, is used for a posteriori error analysis. Application to conforming, nonconforming and mixed finite element methods for an elliptic model problem are discussed.

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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