Runge-Kutta convolution coercivity and its use for time-dependent boundary integral equations (Christian Lubich, Tuebingen)

30.10.2017 15:15

A coercivity property of temporal convolution operators is an essential tool in the analysis of time-dependent boundary integral equations and their space and time discretisations. It is known that this coercivity property is inherited by convolution quadrature time discretisation based on A-stable multistep methods, which are of order at most two. Here we study the question as to which Runge–Kutta-based convolution quadrature methods inherit the convolution coercivity property. It is shown that this holds without any restriction for the third-order Radau IIA method, and on permitting a shift in the Laplace domain variable, this holds for all algebraically stable Runge–Kutta methods and hence for methods of arbitrary order. As an illustration, the discrete convolution coercivity is used to analyse the stability and convergence properties of the time discretisation of a non-linear boundary integral equation that originates from a non-linear scattering problem for the linear wave equation. The talk is based on joint work with Lehel Banjai.

Lieu

salle 623, Séminaire d'analyse numérique

Organisé par

Section de mathématiques

Intervenants

Christian Lubich, University of Tuebingen

entrée libre

Classement

Catégorie: Séminaire

Mots clés: analyse numérique