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A numerical study of a posteriori error estimators for convection-diffusion equations. (English) Zbl 0973.76049
Summary: This paper presents a numerical study of a posteriori error estimators for convection-diffusion equations. The study involves the gradient indicator, an a posteriori error estimator which is based on gradient recovery, three residual-based error estimators for different norms, and two error estimators which are defined by solutions of local Neumann problems. They are compared with respect to the reliable estimation of global error and with respect to the accuracy of computed solutions on adaptively refined grids. The numerical study shows for both criteria of comparison that none of the considered error estimators works satisfactorily in all tests.

76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
65N15 Error bounds for boundary value problems involving PDEs
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