A finite element semi-Lagrangian explicit Runge-Kutta-Chebyshev method for convection dominated reaction-diffusion problems

Explicit Runge-Kutta-Chebyshev methods have proved to be efficient for reaction-diffusion problems of moderate stiffness. In this paper, we extend such an efficiency to convection-dominated-reaction-diffusion problems by giving a formulation of these methods in a semi-Lagrangian framework, using C-0-finite elements of degree m greater than or equal to 2 as the space discretization method. We also study the convergence in the L-2-norm of the methods proposed in this paper. (C) 2003 Elsevier Science B.V. All rights reserved.