On the Equivalence of Semi-Lagrangian Schemes and Particle-in-Cell Finite Element Methods

Abstract

It is shown that the semi-Lagrangian schemes with cubic spline interpolation are equivalent to a particle-in-cell finite element method. The method conserves mass, is unconditionally stable, and has a truncation error as high as fourth-order for smooth enough functions. An efficient computational algorithm for the implementation of the method using B-splines is described.