One-step Taylor-Galerkin methods for convection-diffusion problems

• Autores: Bernardino Roig Sala
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 204, Nº 1, 2007, págs. 95-101
• Idioma: inglés
• DOI: 10.1016/j.cam.2006.04.031
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• Resumen

  • Third and fourth order Taylor-Galerkin schemes have shown to be efficient finite element schemes for the numerical simulation of time-dependent convective transport problems. By contrast, the application of higher-order Taylor-Galerkin schemes to mixed problems describing transient transport by both convection and diffusion appears to be much more difficult. In this paper we develop two new Taylor-Galerkin schemes maintaining the accuracy properties and improving the stability restrictions in convection-diffusion. We also present an efficient algorithm for solving the resulting system of the finite element method. Finally we present two numerical simulations that confirm the properties of the methods.