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On the numerical solution of convection dominated convection-diffusion problems. (English) Zbl 0551.76077
Mathematical methods in energy research, Proc. Spec. Year, Univ. Wyoming 1982-83, 3-21 (1984).
[For the entire collection see Zbl 0546.00029.]
A modified form using an embedding method simplifies the presentation of the streamlined diffusion finite element method of T. J. R. Hughes and A. Brooks [Finite element methods for convection dominated flows, Winter ann. Meet. ASME, New York 1979, AMD Vol. 34, 19-35 (1979; Zbl 0423.76067)] for the numerical solution of convection dominated convection-diffusion flow problems. The modification also makes it clearer which types of boundary conditions are to choose in connection with a method of separating the layer part calculation of the solution. We discuss also more classical methods, such as exponentially upwinded Galerkin methods and a new defect-correction method.

MSC:
76R99 Diffusion and convection
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M99 Basic methods in fluid mechanics