Analysis of Semi-Implicit Runge-Kutta-DGFEM for a Semilinear Convection-Diffusion Equation

作者：Dolejsi Vit^*; V****k Miloslav; V****kova Zuzana

来源：International Conference on Numerical Analysis and Applied Mathematics, 2010-09-19 to 2010-09-25.

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

We deal with the numerical solution of a scalar semilinear convection-diffusion equation, which represents a simplified model to the compressible Navier-Stokes equations. For discretization in space we use the discontinuous Galerkin finite element method (DGFEM) which is a promising scheme for solving problems with shocks and boundary layers. For the time discretizaticn we use implicit Runge-Kutta methods to obtain the scheme which should be able to solve stiff problems in combination with some suitable explicit linearization for treatment of nonlinear terms. The resulting scheme is sufficiently robust and needs only solution of a linear problem at each time step. We present a priori error estimate.