Analysis of semi-implicit Runge-Kutta-DGFEM for a semilinear convection-diffusion equation

Abstract

We deal with the numerical solution of the semilinear convection-diffusion equation. The space discretization is carried out by discontinuous Galerkin finite element method and for the time discretization we employ suitable combination of implicit and explicit Runge-Kutta method.

The resulting scheme is robust and very effective.

Keywords

• a priori error estimates
• discontinuous Galerkin finite element method
• Runge-Kutta method
• semi-implicit scheme