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arXiv · 2604.01200

A Posteriori Error Analysis of Runge-Kutta Discontinuous Galerkin Schemes with SIAC Post-Processing for Nonlinear Convection-Diffusion Systems

Jan Giesselmann·Kiwoong Kwon·Sebastian Krumscheid
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Abstract

We develop reliable a posteriori error estimators for fully discrete Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems endowed with a convex entropy in multiple spatial dimensions on the flat torus T^d, with a focus on the convection-dominated regime. In order to use the relative entropy method, we reconstruct the numerical solution via tensor-product Smoothness-Increasing Accuracy-Conserving (SIAC) filtering which has superconvergence properties. We then derive reliable a posteriori error estimators for the difference between the entropy weak solution and the reconstruction, with constants that are uniform in the vanishing viscosity limit. Our numerical experiments show that the a posteriori error bounds converge with the same order as the error of the reconstructed numerical solution.

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Jan Giesselmann, Kiwoong Kwon, Sebastian Krumscheid. 2026-04-01. A Posteriori Error Analysis of Runge-Kutta Discontinuous Galerkin Schemes with SIAC Post-Processing for Nonlinear Convection-Diffusion Systems. https://arxiv.org/abs/2604.01200

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