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

Authors:
Rodolfo Bermejo;Mofdi El Amrani
Affiliations:
Universidad de Castilla-La Mancha, Dpto. de Matemáticas, Facultad de Ciencias Ambientales Avda. Carlos III s/n, 45071 Toledo, Spain;Universidad Complutense de Madrid, Facultad de CC Matemáticas, Departamento de Matemática Aplicada, 28040 Madrid, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

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 C0-finite elements of degree m ≥ 2 as the space discretization method. We also study the convergence in the L2-norm of the methods proposed in this paper.