Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains
Numerical Analysis
2023-07-06 v1
Abstract
This paper presents the first analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. The analysis is based on non-standard local trace and inverse inequalities that are anisotropic in the spatial and time steps. We prove well-posedness of the discrete problem and provide a priori error estimates in a mesh-dependent norm. Convergence theory is validated by a numerical example solving the advection--diffusion problem on a time-dependent domain for approximations of various polynomial degree.
Keywords
Cite
@article{arxiv.1812.00216,
title = {Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains},
author = {Keegan L. A. Kirk and Tamas L. Horvath and Aycil Cesmelioglu and Sander Rhebergen},
journal= {arXiv preprint arXiv:1812.00216},
year = {2023}
}