Stability and convergence of mixed discontinuous finite element methods for second-order differential problems

被引：10

作者：

Chen, H. ^{[1
]}

Chen, Z. ^{[2
]}

机构：

[1] Department of Mathematics, University of Wyoming, Laramie

[2] Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156

来源：

Journal of Numerical Mathematics | 2003年 / 11卷 / 04期

关键词：

Characteristics; Convergence; Error estimates; Mixed discontinuous finite element methods; Second-order problems; Stability;

D O I：

10.1163/156939503322663449

中图分类号：

学科分类号：

摘要：

In this paper we develop an abstract theory for stability and convergence of mixed discontinuous finite element methods for second-order partial differential problems. This theory is then applied to various examples, with an emphasis on different combinations of mixed finite element spaces. Elliptic, parabolic, and convection-dominated diffusion problems are considered. The examples include classical mixed finite element methods in the discontinuous setting, local discontinuous Galerkin methods, and their penalized (stabilized) versions. For the convection-dominated diffusion problems, a characteristics-based approach is combined with the mixed discontinuous methods.

引用

页码：253 / 287

页数：34

共 21 条

[1]

Agmon S., Lectures on Elliptic Boundary Value Problems, (1965)

[2]

Arbogast T., Wheeler M.F., A characteristics-mixed finite element for advection-dominated transport problems, SIAM J. Numer. Anal., 32, pp. 404-424, (1995)

[3]

Arnold D.N., Breezi F., Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates, RAIRO Modèl. Math. Anal. Numér, 19, pp. 7-32, (1985)

[4]

Arnold D.N., Breezi F., Cockburn B., Marini L.D., Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39, pp. 1749-1779, (2001)

[5]

Bassi F., Rebay S., A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, J. Comp. Phys., 131, pp. 267-279, (1997)

[6]

Brezzi F., Douglas Jr. J., Duran R., Fortin M., Mixed finite elements for second order elliptic problems in three variables, Numer. Math., 51, pp. 237-250, (1987)

[7]

Brezzi F., Douglas Jr. J., Fortin M., Marini L.D., Efficient rectangular mixed finite elements in two and three space variables, RAIRO Modèl. Math. Anal. Numér, 21, pp. 581-604, (1987)

[8]

Brezzi F., Douglas Jr. J., Marini L.D., Two families of mixed finite elements for second order elliptic problems, Numer. Math., 47, pp. 217-235, (1985)

[9]

Brezzi F., Fortin M., Mixed and Hybrid Finite Element Methods, (1991)

[10]

Chen H., Chen Z., Li B., Numerical study of the hp version of mixed discontinuous finite element methods for reaction-diffusion problems: The 1D case, Numer. Meth. Partial Diff. Equations, 19, pp. 525-553, (2003)

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