Space-time hybridizable discontinuous Galerkin method for advection-diffusion on deforming domains: The advection-dominated regime

Abstract

We analyze a space-time hybridizable discontinuous Galerkin method to solve the time-dependent advection-diffusion equation on deforming domains. We prove stability of the discretization in the advection-dominated regime by using weighted test functions and derive a priori space-time error estimates. A numerical example illustrates the theoretical results.