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

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  • 1 The University of British Columbia, Mathematics Department, Vancouver, British Columbia, Canada
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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.

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.

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