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 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.