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COMPARISON OF FINITE VOLUME AND FINITE DIFFERENCE METHODS AND APPLICATION

Analysis and Applications, 2006
In this article, we consider finite volume methods based on a non-uniform grid. Finite volume methods are compared to finite difference methods based on a related grid. As an application, various convergence results are proved for the finite volume function spaces and for some model elliptic and parabolic boundary value problems using these ...
Faure, Sylvain   +2 more
openaire   +1 more source

Zonal Multiscale Finite-Volume framework

Journal of Computational Physics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Davide Cortinovis, Patrick Jenny
openaire   +1 more source

Finite Element and Finite Volume Methods

2009
In this chapter we consider finite element and finite volume discretisations of $$Lu\,: = - \varepsilon u'' - bu' + cu = f\,\,{\rm in}\,(0,1), \,\,\ u(0) = u (1) = 0,$$ with b ≥ β > 0. Its associated variational formulation is: Find \(u \in H_0^1 (0,1)\) such that $$a(u, v) = f(v)\,\,\, {\rm for\, all}\,\, v \in H_0^1 (0,1),$$ (5.2 ...
openaire   +1 more source

Finite-Volume Methods

2001
In Chapter 3, we saw how to derive finite-difference approximations to arbitrary derivatives. In Chapter 4, we saw that the application of a finite-difference approximation to the spatial derivatives in our model PDE’s produces a coupled set of ODE’s.
H. Lomax   +2 more
openaire   +1 more source

On several numerical strategies to solve Richards’ equation in heterogeneous media with finite volumes

Computational Geosciences, 2022
Quang Huy Tran   +2 more
exaly  

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