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FINITE VOLUME SCHEMES FOR DIFFUSION EQUATIONS: INTRODUCTION TO AND REVIEW OF MODERN METHODS

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00813613
Contributor : Jerome Droniou <>
Submitted on : Friday, February 7, 2014 - 11:38:04 AM
Last modification on : Wednesday, January 29, 2020 - 11:58:04 AM
Long-term archiving on: : Monday, May 12, 2014 - 11:56:15 AM

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Jerome Droniou. FINITE VOLUME SCHEMES FOR DIFFUSION EQUATIONS: INTRODUCTION TO AND REVIEW OF MODERN METHODS. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014, 24 (8), pp.1575-1619. ⟨10.1142/S0218202514400041⟩. ⟨hal-00813613v3⟩

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