In this paper we present an analytical, parameter-free, Petrov-Galerkin method that gives stable solutions of convection dominated boundary-value problems. We call it the Best Approximation Weighted Residuals (BAWR) method since it gives the best approximation in the norm induced by the inner-product used to build the weighted-residuals approximation. The method computes the optimal weighting functions by solving suitable adjoint problems. Moreover, through a localization technique it becomes computationally efficient without loosing accuracy. The analysis is confirmed by numerical results.
The Best-Approximation Weighted-Residuals Method for the steady convection diffusion reaction problem
MARCUZZI, FABIO;
2011
Abstract
In this paper we present an analytical, parameter-free, Petrov-Galerkin method that gives stable solutions of convection dominated boundary-value problems. We call it the Best Approximation Weighted Residuals (BAWR) method since it gives the best approximation in the norm induced by the inner-product used to build the weighted-residuals approximation. The method computes the optimal weighting functions by solving suitable adjoint problems. Moreover, through a localization technique it becomes computationally efficient without loosing accuracy. The analysis is confirmed by numerical results.File in questo prodotto:
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