Abstract
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.
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Project supported by the National Natural Science Foundation of China (Nos. 10871156 and 11171269) and the Fund of Xi’an Jiaotong University (No. 2009xjtujc30)
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Zhang, Yz., Hou, Yr. & Wei, Hb. Adaptive mixed least squares Galerkin/Petrov finite element method for stationary conduction convection problems. Appl. Math. Mech.-Engl. Ed. 32, 1269–1286 (2011). https://doi.org/10.1007/s10483-011-1499-6
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DOI: https://doi.org/10.1007/s10483-011-1499-6
Key words
- conduction convection problem
- posteriori error analysis
- mixed finite element
- adaptive finite element
- least squares Galerkin/Petrov method