On Particles and Splines in Bounded Domains

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 $W^{s,p}$-norms, $s\in \mathbb{R}$, $1<p\le \infty$.

20 pages, 3 figures

References in corpus (2)

• Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations
• A Smooth Partition of Unity Finite Element Method for Vortex Particle Regularization