Spurious oscillations reduction in transient diffusion and wave propagation problems discretized with the Finite Element Method

Abstract

This work presents a new method, the SOR_FEM, spurious oscillation reduction-FEM, that uses analytical solutions of simple problems to find numerical solutions of more complex problems to reduce the spurious oscillations that occur due to solution discontinuity. With the proposed method it is possible to find numerical solutions without spurious oscillations of problems submitted to impulsive point sources without using any approximation for the Dirac delta function. To validate the proposed method, linear problems of heat diffusion and wave propagation in homogeneous and heterogeneous media are solved with the Finite Element Method (FEM).