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

Bernardino Roig Sala

• 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.