Using deep neural networks for detecting spurious oscillations in discontinuous Galerkin solutions of convection-dominated convection-diffusion equations

Abstract

Standard discontinuous Galerkin (DG) finite element solutions to convection-dominated convection-diffusion equations usually possess sharp layers but also exhibit large spurious oscillations. Slope limiters are known as a post-processing technique to reduce these unphysical values. This paper studies the application of deep neural networks for detecting mesh cells on which slope limiters should be applied. The networks are trained with data obtained from simulations of a standard benchmark problem with linear finite elements. It is investigated how they perform when applied to discrete solutions obtained with higher order finite elements and to solutions for a different benchmark problem.