Report 1996-05

Higher order discretisation of initial-boundary value problems for mixed systems

R. Bodenmann and H.J. Schroll

Abstract: An initial-boundary value problem for a system of nonlinear partial differential equations, which consists of a hyperbolic and a parabolic part, is taken into consideration. Spacial derivatives are discretised by third order consistent difference operators, which are constructed such that a summation by parts formula holds. Therefore the space discretisation is energy bounded and algebraically stable implicit Runge-Kutta methods can be applied to integrate in time. Boundary layers arising from the artificial boundary conditions are analysed and nonlinear convergence is proved.

Keywords: Higher order difference method, initial-boundary value problem, boundary layer, nonlinear hyperbolic-parabolic system, local stability, convergence.

Paper: Available as PDF (11 MB) or as hardcopy to order reports@sam.math.ethz.ch.