Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3

Numerische Analyse äquivarianter Evolutionsgleichungen

05-017 Vera Thümmler.
Numerical approximation of relative equilibria for equivariant PDEs

In this paper we prove convergence results for the numerical approximation of relative equilibria of equivariant evolution equations with finite differences on an finite equidistant grid with appropriate boundary conditions. Moreover, we consider the approximation of isolated eigenvalues of finite multiplicity of the linear operator which arises from linearization at the equilibrium as well as the approximation of the corresponding invariant subspace. The results in this paper are illustrated by numerical computations for the quintic complex Ginzburg Landau equation.