A Python framework for solving advection-diffusion problems. (English) Zbl 1454.65084

Klöfkorn, Robert (ed.) et al., Finite volumes for complex applications IX – methods, theoretical aspects, examples. FVCA 9, Bergen, Norway, June 15–19, 2020. In 2 volumes. Volume I and II. Cham: Springer. Springer Proc. Math. Stat. 323, 695-703 (2020).
The authors introduce a Python layer for the DUNE-FEM-DG module [A. Dedner et al., “The DUNE-FEM-DG module”, ANS 5, No. 1, 21–62 (2017; doi:10.11588/ans.2017.1.28602)] which is available open-source and provides highly efficient implementations of the Discontinuous Galerkin (DG) method for solving a wide range of non linear PDEs (Partial Differential Equations). Although the C++ interfaces of Dune-Fem-DG are highly flexible and customizable but a good knowledge of C++ is necessary to make use of this powerful tool. In this paper, some easy interfaces based on Python and the Unified Form Language are provided to open Dune-Fem-DG. The Python interfaces are demonstrated for parabolic and first order hyperbolic PDEs. This work is interesting and useful.
For the entire collection see [Zbl 1445.65003].


65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
76N30 Waves in compressible fluids
35Q31 Euler equations
Full Text: DOI


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