Numerical validation of a preliminar error analysis of the Particle Finite Element Method and its comparison against an Eulerian formulation

Abstract

The main goal of this paper is to validate experimentally the principal conclusions previuoslypublished in [1]. Two manufactured test cases were considered with their respective analytic solu-tions. First, an scalar transport equation is taken written in such a way that several parameters areincluded to stress the limits where the Eulerian and the Lagrangian approaches behave better. Theresults show the conditions to be fulfilled to choose between both formulations according to the prob-lem parameters. A brief discussion about the projection needed for PFEM-2 method is included,specially due to its impact on the error convergence rate. Laterly, an extension to Navier-Stokesequations is introduced using also a manufactured case to verify again the same conclusions. This paper intends to establish the first steps towards a mathematical error analysis for the Particle FiniteElement Method in order to justify the preliminar theoretical and experimental results presented inthis paper.