A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlin...A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.展开更多
In this paper, the convergence analysis of the famous Carey element in 3-D is studied on anisotropic meshes. The optimal error estimate is obtained based on some novel techniques and approach, which extends its applic...In this paper, the convergence analysis of the famous Carey element in 3-D is studied on anisotropic meshes. The optimal error estimate is obtained based on some novel techniques and approach, which extends its applications.展开更多
In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic fi...In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic finite volume schemes. Then we present our recent advances on finite volume schemes of arbitrary order. For each scheme, we first explain its construction and then perform its error analysis under both HI and L2 norms along with study of superconvergence properties.展开更多
文摘A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
文摘In this paper, the convergence analysis of the famous Carey element in 3-D is studied on anisotropic meshes. The optimal error estimate is obtained based on some novel techniques and approach, which extends its applications.
基金supported by National Science Foundation of USA(Grant No.DMS1115530)National Natural Science Foundation of China(Grant No.11171359)the Fundamental Research Funds for the Central Universities of China
文摘In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic finite volume schemes. Then we present our recent advances on finite volume schemes of arbitrary order. For each scheme, we first explain its construction and then perform its error analysis under both HI and L2 norms along with study of superconvergence properties.
