Finite element methods for convection-diffusion problems. (English) Zbl 0505.76099

Johnson, Claes

Computing methods in applied sciences and engineering V, Proc. 5th int. Symp., Versailles 1981, 311-323 (1982).

Summary: We give a survey of some recent results for finite element methods for first order linear hyperbolic problems. In particular we discuss a new finite element method for convection dominated convection-diffusion problems, the streamline diffusion method, which is higher order accurate and has good stability properties. We also present improved estimates for the fully discontinuous Galerkin method by Lesaint-Raviart and give extensions to Friedrichs’ systems.
For the entire collection see [Zbl 0498.00007].

MSC:

76R99	Diffusion and convection
76R50	Diffusion
76M10	Finite element methods applied to problems in fluid mechanics
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

first order linear hyperbolic problems; streamline diffusion method; stability; fully discontinuous Galerkin method of Lesaint-Raviart; Friedrichs’ systems

Citations:

Zbl 0498.00007