On particles and splines in bounded domains

ESAIM Mathematical Modelling and Numerical Analysis, vol. 55, pp. S301–S321

Abstract

We propose numerical schemes that enable the application of particle methods for advection problems in general bounded domains. These schemes combine particle fields with Cartesian tensor product splines and a fictitious domain approach. Their implementation only requires a fitted mesh of the domain’s boundary, and not the domain itself, where an unfitted Cartesian grid is used. We establish the stability and consistency of these schemes in Ws,p-norms, s ∈ ℝ, 1 ≤ p ≤ ∞.

Authors 1

1. Matthias Kirchhart corresponding Aachen Center for Computational Engineering Science Mathematics Division

   RWTH Aachen University

   Affiliation as printed

   Center for Computational Engineering Science, Mathematics Division, RWTH Aachen University, Aachen, Germany