This paper deals with a numerical approximation of a bifurcation problem with corank 2. In the neighborhood of the bifurcation point the nonlinear equation is embedded into an extended system. The… (More)

We consider linear operator equations Lf = g in the context of boundary element methods, where the operator L is equivariant i.e., commutes with the actions of a given finite symmetry group. By… (More)

A grid strategy is developed via the first step of a defect correction applied to the Kreiss method. The full defect corrections are used on the final grid to compute high accuracy approximations… (More)

This lecture is an appetizer for my two books in OUP: Numerical Methods for Nonlinear Elliptic Differential Equations, A Synopsis, Numerical Methods for Bifurcation and Center Manifolds in Nonlinear… (More)

This paper extends for the first time Schaback’s linear discretization theory to nonlinear operator equations, relying heavily on the methods in Böhmer’s 2010 book. There is no restriction to… (More)

A numerical tool for the detection of degenerated symmetry breaking bifurcation points is presented. The degeneracies are classified and numerically processed on 1-D restrictions of the bifurcation… (More)

We give a simple approach for a well-known, but rather complicated theory for general discretization methods, Petryshyn [34] and Zeidler [40]. We employ only some basic concepts such as… (More)