Generalized Galerkin Methods for Convection-Dominated Problems

1989 ◽  
pp. 177-195
Author(s):  
J. Donea
Keyword(s):  
Galerkin Methods ◽  
Convection Dominated

Feedback Petrov-Galerkin methods for convection-dominated problems

1991 ◽  
Vol 88 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Eduardo Gomes Dutra Do Carmo ◽  
Augusto Cesar Galeão
Keyword(s):  
Galerkin Methods ◽  
Convection Dominated

Generalized Galerkin Methods for Convection Dominated Transport Phenomena

1991 ◽  
Vol 44 (5) ◽  
pp. 205-214 ◽  
Author(s):  
J. Donea
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Transport Phenomena ◽  
Galerkin Methods ◽  
Approximation Properties ◽  
Weighted Residuals ◽  
Convection Dominated

A brief survey is made of recent advances in the development of finite element methods for convection dominated transport phenomena. Because of the nonsymmetric character of convection operators, the standard Galerkin formulation of the method of weighted residuals does not possess optimal approximation properties in application 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 a special emphasis on the major breakthroughs represented by the so-called streamline upwind Petrov-Galerkin and Galerkin least-squares methods. The second part of the paper is devoted to a review of time-accurate finite element methods recently developed for the solution of unsteady problems governed by first-order hyperbolic equations. This includes Petrov-Galerkin, Taylor-Galerkin, least-squares, and various characteristic Galerkin methods. The extension of these methods to deal with unsteady convection-diffusion problems is also considered.

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