Galerkin-Runge-Kutta methods and hyperbolic initial boundary value problems

Abstract

Inhomogeneous but time-homogeneous linear hyperbolic initial boundary value problems are solved using Galerkin procedures for the space discretization and Runge-Kutta methods for the time discretization. The space discretized system is not transformed a-priori in a linear system of first order. For the difference of the Ritz projection of the exact solution and the numerical approximation error estimates are derived under the assumption that the applied Runge-Kutta methods have a non-empty interval of absolute stability. It is shown that this class of schemes is not empty in the present case of second order systems, too.