A FINITE VOLUME METHOD FOR THE LAPLACE EQUATION ON ALMOST ARBITRARY TWO-DIMENSIONAL GRIDS

By Komla Domelevo, Pascal Omnes. 2005

268 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/a838f2706fe2eb983a7f10f3509f985f3cb9d818

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In Computational Mechanics

In Electrical and Electronic Engineering

Citations in the corpus

Stabilized DDFV schemes for stokes problem with variable viscosity on general 2D meshes (2011, methodology): “The DDFV schemes have been first introduced and studied in [9,11] to approximate the solution of the Laplace equation on a large class of 2D meshes including nonconformal and distorted meshes, without “orthogonality” assumptions as for classical finite volume methods.”
Finite Volume Methods: Foundation and Analysis (2004, methodology): “Utilizing these techniques, convergence of finite volume schemes (uniform with respect to ε→ 0) was proved in Eymard et al. (2002) and error estimates were obtained for viscous approximations in Evje and Karlsen (2002) and Eymard, Gallouët and Herbin (2002).”
A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis (2007, background): “However, for general meshes or anistropic diffusion operators, the construction of an approximation to the normal flux is more strenuous [2, 3, 7]; it is often performed by the reconstruction of a discrete gradient, either in the edges of the cell, or in the cell itself.”
A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension (2006, methodology): “Still in 2D, a technique using dual meshes is introduced in Domelevo & Omnes (2005) and Hermeline (2000), which generalizes the idea of Hu & Nicolaides (1992) and Nicolaides (1992) for div–curl problems to meshes with no orthogonality conditions; however, the use of a dual mesh renders the scheme…”
Mimetic finite difference method (2014, methodology): “Instead, an exact duality relation is satisfied by the discrete duality finite volume (DDFV) method for two-dimensional diffusion problems in [95,136,137].”
Small-stencil 3D schemes for diffusive flows in porous media (2012, methodology): “The DDFV scheme, see [22, 14, 9] for the two dimensional case and [23, 11, 12, 24, 6, 10, 7] for the three dimensional case may also be seen as a gradient scheme.”
Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes (2007, methodology): “We consider in this paper the class of finite volume schemes introduced by Hermeline in [24], by Domelevo, Omnès in [13] for the Laplace equation and in [11] for other linear equations like the Stokes or the Div-Curl system.”
ASYMPTOTIC AND NUMERICAL MODELLING OF FLOWS IN FRACTURED POROUS MEDIA (2009, methodology): “To this end, we choose a Discrete Duality Finite Volume approach (see [2,14]) which consists in approximating the solution simultaneously on a primal and a dual mesh.”
Analysis of a finite volume method for a cross-diffusion model in population dynamics (2011, unknown): “For instance, for the so-called DDFV schemes (see Hermeline [31], Domelevo and Omnès [18], Andreianov, Bendahmane and Karlsen [4] and references therein) or the “complementary volumes” schemes such as those of Afif and Amaziane [1] and Handlovičová, Mikula and Sgallari [30], the lemma can be stat”