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Footbridge between finite volumes and finite elements with applications to CFD
Author(s) -
Pascal Frédéric,
Ghidaglia JeanMichel
Publication year - 2001
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.199
Subject(s) - finite volume method , computational fluid dynamics , discretization , finite element method , polygon mesh , finite volume method for one dimensional steady state diffusion , partial differential equation , mathematics , context (archaeology) , navier–stokes equations , representation (politics) , mesh generation , compressibility , computer science , mathematical optimization , mathematical analysis , numerical partial differential equations , geometry , mechanics , physics , paleontology , biology , politics , political science , law , thermodynamics
The aim of this paper is to introduce a new algorithm for the discretization of second‐order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier–Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright © 2001 John Wiley & Sons, Ltd.