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Adaptive mixed least squares Galerkin/Petrov finite element method for stationary conduction convection problems. (English) Zbl 1237.76078

Summary: An adaptive mixed least squares Galerkin/Petrov finite element method (FEM) is developed for stationary conduction convection problems. The mixed least squares Galerkin/Petrov FEM is consistent and stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. Using the general theory of Verfürth, the posteriori error estimates of the residual type are derived. Finally, numerical tests are presented to illustrate the effectiveness of the method.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65Z05 Applications to the sciences

Software:

FreeFem++
PDFBibTeX XMLCite
Full Text: DOI

References:

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