A python framework for solving advection-diffusion problems

Abstract

This paper discusses a Python interface for the recently published Dune-Fem-DG module which provides highly efficient implementations of the Discontinuous Galerkin (DG) method for solving a wide range of non linear partial differential equations (PDE). Although the C++ interfaces of Dune-Fem-DG are highly flexible and customizable, a solid knowledge of C++ is necessary to make use of this powerful tool. With this work easier user interfaces based on Python and the Unified Form Language are provided to open Dune-Fem-DG for a broader audience. The Python interfaces are demonstrated for both parabolic and first order hyperbolic PDEs.