A Discontinuous Galerkin method for Shock Capturing using a mixed high-order and sub-grid low-order approximation space

2019/11/04 by Persson, Per-Olof, Stamm, Benjamin
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1911.01095

Abstract

This article considers a new discretization scheme for conservation laws. The discretization setting is based on a discontinuous Galerkin scheme in combination with an approximation space that contains high-order polynomial modes as well as piece-wise constant modes on a sub-grid. The high-order modes can continuously be suppressed with a penalty function that is based on a sensor which is intertwined with the approximation space. Numerical tests finally illustrate the performance of this scheme.

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