Hyperbolic Problems

Abstract

The numeical approximation of hyperbolic equations is a v ery active area of reasearch. The main distinguishing feature of these initial-boundary value problems is the fact that perturbations propagate with finite speed. Another characterizing aspect is that the boundary treatment is not as simple as that for elliptic or parabolic equations. According to the sign of the equation coefficients, the inflow and outflow boundary regions determine, from case to case, where boundary conditions have to be prescribed. The situation becomes more complex for systems of hyperbolic equations, where the boundary treatment must undergo a local characteristic analysis. If not implemented conveniently, the numerical realization of boundary conditions is a potential source of spurious instabilities.