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International Journal for Multiscale Computational Engineering

年間 6 号発行

ISSN 印刷: 1543-1649

ISSN オンライン: 1940-4352

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Indexed in

PSEUDO-MULTI-SCALE FUNCTIONS FOR THE STABILIZATION OF CONVECTION-DIFFUSION EQUATIONS ON RECTANGULAR GRIDS

巻 11, 発行 4, 2013, pp. 319-331
DOI: 10.1615/IntJMultCompEng.2012004234
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要約

We propose a finite element method of Petrov-Galerkin type for a singularly perturbed convection diffusion problem on a discretization consisting of rectangular elements. The method is based on enriching the finite-element space with a combination of multiscale and residual-free bubble functions. These functions require the solution of the original differential problem, which makes the method quite expensive, especially in two dimensions. Therefore, we instead employ their cheap, yet efficient approximations, using only a few nodes in each element. Several numerical tests confirm the good performance of the corresponding numerical method.

参考
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  20. Sangalli, G., Global and local error analysis for the residual-free bubbles method applied to advection-dominated problems. DOI: 10.1137/S0036142999365382

によって引用された
  1. Baysal Onur, Bubble and multiscale stabilization of bilinear finite element methods for transient advection–diffusion equations on rectangular grids, Journal of Computational and Applied Mathematics, 259, 2014. Crossref

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