Local time stepping methods and discontinuous Galerkin methods applied to diffusion advection reaction equations
It provides a numerical solver for challenging DARE problems with localized features, but the contribution is incremental as it combines existing methods.
The paper develops multilevel local time stepping methods combined with discontinuous Galerkin discretization for diffusion-advection-reaction equations, demonstrating efficiency on cyclic voltammetry and fracture flow problems.
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.