A posteriori error analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem

2024/04/05 by Wang, Yuan, Rhebergen, Sander
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2404.04130

Abstract

We present and analyze an a posteriori error estimator for a space-time hybridizable discontinuous Galerkin discretization of the time-dependent advection-diffusion problem. The residual-based error estimator is proven to be reliable and locally efficient. In the reliability analysis we combine a Peclet-robust coercivity type result and a saturation assumption, while local efficiency analysis is based on using bubble functions. The analysis considers both local space and time adaptivity and is verified by numerical simulations on problems which include boundary and interior layers.

Related

• Space-time hybridizable discontinuous Galerkin method for advection-diffusion on deforming domains: The advection-dominated regime
• Robust a Posteriori Error Estimates for HDG method for Convection-Diffusion Equations
• An a posteriori error estimator for discontinuous Galerkin methods for non-stationary convection-diffusion problems
• A posteriori analysis for nonlinear convection-diffusion systems
• Adaptive discontinuous Galerkin methods for nonlinear parabolic problems