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

  • Daniele A. Di PietroEmail author
  • Jean-Marc Gratien
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)


In this work we propose an original point of view on lowest order methods for diffusive problems which lays 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 omitted to help the reader unfamiliar with advanced C +  + programming techniques.


Lowest-order methods Domain specific embedded language Petrov-Galerkin methods cell centered Galerkin methods hybrid finite volume methods 


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Fruitful discussions with Christophe Prud’homme (Laboratoire Jean Kuntzmann, University of Grenoble) are gratefully acknowledged. We also wish to thank all the contributors to the Arcane platform.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.IFP Energies nouvellesRueil-MalmaisonFrance

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