With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions （ABCs） for heat equation. We prove...With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions （ABCs） for heat equation. We proved that the coupled system yields a stable problem between the obtained high-order local ABCs and the partial differential equation in the computational domain. This method has been used widely in wave propagation models only recently. We extend the spirit of the methodology to parabolic ones, which will become a basis to design the local ABCs for a class of nonlinear PDEs. Some numerical tests show that the new treatment is very efficient and tractable.展开更多
Abstract. In this paper which is motivated by computation on parallel machine, we showthat the superconvergence results of the finite element method(FEM) with Lagrange mul-tipliers based on domain decomposition method...Abstract. In this paper which is motivated by computation on parallel machine, we showthat the superconvergence results of the finite element method(FEM) with Lagrange mul-tipliers based on domain decomposition method (DDM) with nonmatching grids can becarried over to parabolic problems. The main idea of this paper is to achieve the combina-tion of parallel computational method with the higher accuracy technique by interpolationfinite element postprocessing.展开更多
文摘With the development of numerical methods the numerical computations require higher and higher accuracy. This paper is devoted to the high-order local absorbing boundary conditions （ABCs） for heat equation. We proved that the coupled system yields a stable problem between the obtained high-order local ABCs and the partial differential equation in the computational domain. This method has been used widely in wave propagation models only recently. We extend the spirit of the methodology to parabolic ones, which will become a basis to design the local ABCs for a class of nonlinear PDEs. Some numerical tests show that the new treatment is very efficient and tractable.
文摘Abstract. In this paper which is motivated by computation on parallel machine, we showthat the superconvergence results of the finite element method(FEM) with Lagrange mul-tipliers based on domain decomposition method (DDM) with nonmatching grids can becarried over to parabolic problems. The main idea of this paper is to achieve the combina-tion of parallel computational method with the higher accuracy technique by interpolationfinite element postprocessing.
