# Local time stepping methods and discontinuous Galerkin methods applied to diffusion advection reaction equations

## TL;DR

This paper develops local time stepping methods combined with discontinuous Galerkin spatial discretization to efficiently solve complex diffusion advection reaction equations with features like fractures and obstacles, demonstrated through various experiments.

## Contribution

It introduces a multilevel, local time solver for DAREs using DG and advanced time stepping methods, enhancing computational efficiency for complex geometries.

## Key findings

- Efficient solver demonstrated on cyclic voltammetry models.
- Effective handling of fractures and obstacles in fluid flow simulations.
- Significant reduction in computational time compared to traditional methods.

## Abstract

This paper is focussed on the numerical resolution of diffusion advection and reaction equations (DAREs) with special features (such as fractures, walls, corners, obstacles or point loads) which globally, as well as locally, have important effects on the solution. We introduce a multilevel and local time solver of DAREs based on the discontinuous Galerkin (DG) method for the spatial discreization and time stepping methods such as exponential time differencing (ETD), exponential Rosenbrock (EXPR) and implicit Euler (Impl) methods. The efficiency of our solvers is shown with several experiments on cyclic voltammetry models and fluid flows through domains with fractures.