FINITE VOLUME SCHEMES FOR DIFFUSION EQUATIONS: INTRODUCTION TO AND REVIEW OF MODERN METHODS
By Jérôme Droniou. 2014
289 citations recorded by the source corpus.
We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature results, focusing on two important properties of schemes (discrete versions of well-known properties of the continuous equation): coercivity and minimum–maximum principles. Coercivity ensures the stability of the method as well as its convergence under assumptions compatible with real-world applications, whereas minimum–maximum principles are crucial in case of strong anisotropy to obtain physically meaningful approximate solutions.
Subfields: Computational Mechanics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/bc083288236e4c49b480d63266f008576a62cb16
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In Computational Mechanics
- Andrea Borio
- Stefano Berrone
- Gianmarco Manzini
- Paola Francesca Antonietti
- Marco Verani
- Jean-Sylvain Camier
- Luca Formaggia
- Anna Scotti
In Numerical Analysis
- Stefano Berrone
- Paola Francesca Antonietti
- Marco Verani
- Andrea Borio
- Gianmarco Manzini
- Nicola Verzott
- Luca Formaggia
- Anna Scotti
Citations in the corpus
- A monotone nonlinear finite volume method for approximating diffusion operators on general meshes (2016, methodology): “A thorough review of most of these methods is carried out in [22].”
- SUPG stabilization for the nonconforming virtual element method for advection–diffusion–reaction equations (2018, methodology): “Other methods or families of methods that are available from the literature include the polygonal/polyhedral finite element method (PFEM) [32, 33], the BEM-based FEM [34, 35], the finite volume methods [36, 37], hybrid high-order (HHO) method [38], the discontinuous Galerkin (DG) method [39, 40], an”
- MIMETIC FINITE DIFFERENCE APPROXIMATION OF FLOWS IN FRACTURED POROUS MEDIA (2016, methodology): “For more information on the finite volume method, the interested reader may consult [39], or the recent review [35].”