论文信息 - Convergence analysis of an upwind mixed element method for advection diffusion problems

Convergence analysis of an upwind mixed element method for advection diffusion problems

We consider a upwinding mixed element method for a system of first order partial differential equations resulting from the mixed formulation of a general advection diffusion problem. The system can be used to model the transport of a contaminant carried by a flow. We use the lowest order Raviart-Thomas mixed finite element space. We show the first order convergence both for concentration and concentration flux in L^2(@W).

Zhitao Li

[1] Chi-Wang Shu,et al. Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems , 2001, J. Sci. Comput..

[2] Panayot S. Vassilevski,et al. An Upwinding Cell-Centered Method with Piecewise Constant Velocity over Covolumes , 1999 .

[3] V. Thomée,et al. Error estimates for some mixed finite element methods for parabolic type problems , 1981 .

[4] Do Y. Kwak,et al. Mixed Upwinding Covolume Methods on Rectangular Grids for Convection-Diffusion Problems , 1999, SIAM J. Sci. Comput..

[5] Richard E. Ewing,et al. The approximation of the pressure by a mixed method in the simulation of miscible displacement , 1983 .

[6] Huang Jianguo,et al. On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems , 1998 .

[7] Douglas N. Arnold,et al. Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

[8] Michel Fortin,et al. Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[9] Philippe G. Ciarlet,et al. The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[10] Ronghua Li. Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods , 2000 .