This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier tec...This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier technique and is well suited to the no-slip bound ary condition in viscous flow problems. In order to improve the accuracy of solu tions, meshes are refined according to the a posteriori error estimate. The mini -element discretization is applied to solve the generalized Stokes problem. Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition.展开更多
A nonoverlapping domain decomposition iterative procedure is developed and analyzed for generalized Stokes problems and their finite element approximate problems in R^N（N=2,3）. The method is based on a mixed-type co...A nonoverlapping domain decomposition iterative procedure is developed and analyzed for generalized Stokes problems and their finite element approximate problems in R^N（N=2,3）. The method is based on a mixed-type consistency condition with two parameters as a transmission condition together with a derivative-free transmission data updating technique on the artificial interfaces. The method can be applied to a general multi-subdomain decomposition and implemented on parallel machines with local simple communications naturally.展开更多
In this paper, the fundamental solution of rotating generalized Stokes problem in R^3 is established. To obtain it, some fundamental solutions of other problems also are established, such as generalized Laplace proble...In this paper, the fundamental solution of rotating generalized Stokes problem in R^3 is established. To obtain it, some fundamental solutions of other problems also are established, such as generalized Laplace problem, generalized Stokes problem and rotating Stokes problem.展开更多
文摘This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier technique and is well suited to the no-slip bound ary condition in viscous flow problems. In order to improve the accuracy of solu tions, meshes are refined according to the a posteriori error estimate. The mini -element discretization is applied to solve the generalized Stokes problem. Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition.
文摘A nonoverlapping domain decomposition iterative procedure is developed and analyzed for generalized Stokes problems and their finite element approximate problems in R^N（N=2,3）. The method is based on a mixed-type consistency condition with two parameters as a transmission condition together with a derivative-free transmission data updating technique on the artificial interfaces. The method can be applied to a general multi-subdomain decomposition and implemented on parallel machines with local simple communications naturally.
基金Supported by the National Natural Science Foundation of China (No. 10571142)
文摘In this paper, the fundamental solution of rotating generalized Stokes problem in R^3 is established. To obtain it, some fundamental solutions of other problems also are established, such as generalized Laplace problem, generalized Stokes problem and rotating Stokes problem.
