Displaying similar documents to “Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem”

A parameter-free stabilized finite element method for scalar advection-diffusion problems

Pavel Bochev, Kara Peterson (2013)

Open Mathematics

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We formulate and study numerically a new, parameter-free stabilized finite element method for advection-diffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solving simplified one-dimensional versions of the governing equations on the edges. Then we use...

An analysis of the cell vertex method

K. W. Morton, M. Stynes (1994)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids

Komla Domelevo, Pascal Omnes (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present a finite volume method based on the integration of the Laplace equation on both the cells of a primal almost arbitrary two-dimensional mesh and those of a dual mesh obtained by joining the centers of the cells of the primal mesh. The key ingredient is the definition of discrete gradient and divergence operators verifying a discrete Green formula. This method generalizes an existing finite volume method that requires “Voronoi-type” meshes. We show the equivalence of this finite...