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

TL;DR

This paper develops and analyzes a space-time hybridizable discontinuous Galerkin method for advection-diffusion equations on deforming domains, focusing on stability and error estimates in the advection-dominated regime.

Contribution

It introduces a novel space-time HDG method with stability proof and error analysis specifically for deforming domains in advection-dominated scenarios.

Findings

Method is stable in advection-dominated regime

A priori error estimates are derived

Numerical example confirms theoretical results

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.