A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes

Abstract. In this work we propose an original implementation of a large family of lowest-order methods for diffusive problems including standard and hybrid finite volume methods, mimetic finite difference-type schemes, and cell centered Galerkin methods. The key idea is to regard the method at hand as a (Petrov–)Galerkin scheme based on possibly incomplete, broken affine spaces defined from a gradient reconstruction and a point value. The resulting unified framework serves as a basis for the development of a FreeFEM-like domain specific language targeted at defining discrete linear and bilinear forms. Both the back-end and the front-end of the language are extensively discussed, and several examples of applications are provided. The overhead of the language is evaluated by com-paring with a more traditional implementation. A benchmark including the comparison with more classical finite element methods on standard meshes is also proposed. Key words. Domain specific embedded language, finite volume methods, cell centered Galerkin methods, Petrov–Galerkin methods AMS subject classifications. 65N08, 65N30, 65Y05 1. Introduction. Lowest-orde