A Discontinuous Galerkin method for Shock Capturing using a mixed high-order and sub-grid low-order approximation space
Numerical Analysis
2021-10-14 v3 Numerical Analysis
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.
Cite
@article{arxiv.1911.01095,
title = {A Discontinuous Galerkin method for Shock Capturing using a mixed high-order and sub-grid low-order approximation space},
author = {Per-Olof Persson and Benjamin Stamm},
journal= {arXiv preprint arXiv:1911.01095},
year = {2021}
}