In this paper, a semi-discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction-convection problems in two dimension is presented. In this method, we solve the nonlinear e...In this paper, a semi-discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction-convection problems in two dimension is presented. In this method, we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct this solutions on the same grid using a linearized defect-correction technique. The stability and the error analysis are derived. The theory analysis shows that our method is stable and has a good convergence property.展开更多
A nonlinear Galerkin method using spectral expansions is presented for thesteady nonlinear partial differential equations. We prove the existence, uniqueness andconvergence of the numerical solution corresponding to t...A nonlinear Galerkin method using spectral expansions is presented for thesteady nonlinear partial differential equations. We prove the existence, uniqueness andconvergence of the numerical solution corresponding to this method. Compared with the usualGalerkin method, the nonlinear Galerkin method is simpler under the same convergenceaccuracy.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10971166)the National Basic Research Program of China (Grant No. 2005CB321703)
文摘In this paper, a semi-discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction-convection problems in two dimension is presented. In this method, we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct this solutions on the same grid using a linearized defect-correction technique. The stability and the error analysis are derived. The theory analysis shows that our method is stable and has a good convergence property.
文摘A nonlinear Galerkin method using spectral expansions is presented for thesteady nonlinear partial differential equations. We prove the existence, uniqueness andconvergence of the numerical solution corresponding to this method. Compared with the usualGalerkin method, the nonlinear Galerkin method is simpler under the same convergenceaccuracy.
