Generalized Galerkin Methods for Convection-Dominated Problems
A brief survey is presented of generalized Galerkin methods for steady and unsteady convection-dominated problems. The particular areas upon which attention is focused are Petrov-Galerkin methods for steady problems and Taylor-Galerkin methods for evolutionary problems governed by hyperbolic equations. Also discussed are mixed advection-diffusion problems for which a splitting-up method of solution is suggested. Numerical examples are included to illustrate the performance of the Taylor-Galerkin method in the solution of linear and nonlinear hyperbolic problems.
KeywordsGalerkin Method Uniform Mesh Galerkin Approximation Consistent Mass Matrix Artificial Diffusion
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