Time-space adaptive discontinuous Galerkin method for advection-diffusion equations with non-linear reaction mechanism

TL;DR

This paper presents a novel time-space adaptive discontinuous Galerkin method with robust error estimation for solving convection-dominated advection-diffusion equations with non-linear reactions, improving accuracy and efficiency.

Contribution

It introduces a new a posteriori error estimator and applies elliptic reconstruction to enhance adaptive methods for complex reactive transport problems.

Findings

Effective in heterogeneous media

Handles high Péclet numbers robustly

Improves computational efficiency

Abstract

In this work, we apply a time-space adaptive discontinuous Galerkin method using the elliptic reconstruction technique with a robust (in P\'eclet number) elliptic error estimator in space, for the convection dominated parabolic problems with non-linear reaction mechanisms. We derive a posteriori error estimators in the $L^{\infty}(L^2)+L^2(H^1)$-type norm using backward Euler in time and discontinuous Galerkin (symmetric interior penalty Galerkin (SIPG)) in space. Numerical results for advection dominated reactive transport problems in homogeneous and heterogeneous media demonstrate the performance of the time-space adaptive algorithm.