关键词: mixed element method, equation of magnetohydrodynamics, Galerkin-Petrov least squares method, error estimate

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 Babu\v{s}ka-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained.

Key words: mixed element method, Galerkin-Petrov least squares method, error estimate, equation of magnetohydrodynamics