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H. Chen, Z. Chen

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

Keywords: mixed discontinuous finite element methods, second-order problems, stability, convergence, error estimates, characteristics

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 (stablized) versions. For the convection-dominated diffusion problems, a characteristics-based approach is combined with the mixed discontinuous methods.

Journal of Numerical Mathematics, Walter de Gruyter

Print ISSN: 1570-2820
Volume: 11, 12/2003
Pages: 253 - 287

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