Lowest order methods for diffusive problems on general meshes: A unified approach to definition and implementation

Daniele Antonio Di Pietro (1) , Jean-Marc Gratien (1)

1 IFPEN - IFP Energies nouvelles

In this work we propose an original point of view on lowest order methods for diffusive problems which aims at laying the pillars of a C++ multi-physics, FreeFEM-like platform. The key idea is to regard lowest order methods as (Petrov)-Galerkin methods based on possibly incomplete, broken polynomial spaces defined from a gradient reconstruction. After presenting some examples of methods entering the framework, we show how implementation strategies common in the finite element context can be extended relying on the above definition. Several examples are provided throughout the presentation, and programming details are often concealed to help the reader unfamiliar with advanced C++ programming techniques.

Mots clés: Lowest-order methods; Domain specific embedded language; Petrov-Galerkin methods

Domaines: Analyse numérique [math.NA]

Daniele Antonio Di Pietro, Jean-Marc Gratien. Lowest order methods for diffusive problems on general meshes: A unified approach to definition and implementation. Finite Volumes for Complex Applications VI Problems & Perspectives, Springer, pp.803-819, 2011, ⟨10.1007/978-3-642-20671-9_84⟩. ⟨hal-00562500⟩