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Recent advances in the development of finite element methods for convection dominated transport phenomena are reviewed. Due to the nonsymmetric character of convection operators, the standard Galerkin formulation of the method of weighted residuals does not possess optimal approximation properties when applied to problems in this class. As a result, numerical solutions are often corrupted by spurious node-to-node oscillations. For steady problems describing convection and diffusion, spurious oscillations can be precluded by the use of upwind-type finite element approximations that are constructed through a proper Petrov-Galerkin weighted residual formulation. Various upwind finite element formulations are reviewed in this paper, with special emphasis on the major breakthroughs represented by the so-called streamline upwind Petrov-Galerkin and Galerkin least-squares methods. Time-accurate finite element methods recently developed for the solution of unsteady problems governed by first-order hyperbolic equations are discussed. The extension of these methods to deal with unsteady convection-diffusion problems is also considered.

Additional information

Authors: DONEA J, JRC Ispra (IT)
Bibliographic Reference: Article: Applied Mechanics Review, Vol. 44 (1991) No. 5, pp. 205-214
Record Number: 199111087 / Last updated on: 1994-12-02
Original language: en
Available languages: en