Meshless Methods for Conservation Laws

In this article, two meshfree methods for the numerical solution of conservation laws are considered. The Finite Volume Particle Method (FVPM) generalizes the Finite Volume approach and the Finite Pointset Method (FPM) is a Finite Difference scheme which can work on unstructured and moving point clouds. Details of the derivation and numerical examples are presented for the case of incompressible, viscous, two-phase flow. In the case of FVPM, our main focus lies on the derivation of stability estimates.