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arXiv · 1812.00216

Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains

Keegan L. A. Kirk·Tamas L. Horvath·Aycil Cesmelioglu·Sander Rhebergen
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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.

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Keegan L. A. Kirk, Tamas L. Horvath, Aycil Cesmelioglu, Sander Rhebergen. 2018-12-01. Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. https://doi.org/10.1137/18m1202049

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