Time-space adaptive discontinuous Galerkin method for advection-diffusion equations with non-linear reaction mechanism
For researchers solving convection-dominated parabolic problems with non-linear reactions, this provides an adaptive method with rigorous error control, though it is an incremental extension of existing techniques.
This work develops a time-space adaptive discontinuous Galerkin method for advection-diffusion equations with non-linear reaction, using elliptic reconstruction and a robust error estimator. Numerical results demonstrate the performance of the adaptive algorithm for advection-dominated reactive transport problems.
In this work, we apply a time-space adaptive discontinuous Galerkin method using the elliptic reconstruction technique with a robust (in Péclet 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.