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Galerkin-Petrov least squares mixed element method for stationary incompressible magnetohydrodynamics |
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| Authors: | Luo Zhen-dong Mao Yun-kui Zhu Jiang |
| Affiliation: | 1. School of Science,Beijing Jiaotong University,Beijing 100044,P.R.China;Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,P.R.China 2. School of Science,Beijing Jiaotong University,Beijing 100044,P.R.China 3. Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,P.R.China |
| Abstract: | The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least squares mixed finite element format for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of its solution are derived. Through this method, the combination among the mixed finite element spaces does not demand the discrete Babuska-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained. |
| Keywords: | equation of magnetohydrodynamics mixed element method GalerkinPetrov least squares method error estimate |
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