𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Analysis of the Cell-Centred Finite Volume Method for the Diffusion Equation

✍ Scribed by W.P. Jones; K.R. Menzies

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
210 KB
Volume
165
Category
Article
ISSN
0021-9991

No coin nor oath required. For personal study only.

✦ Synopsis

This paper presents a rigorous theoretical analysis of the cell-centred finite volume method for Poisson's equation. We review the traditional Taylor series expansion technique which suggests that the cell-centred method is inconsistent on nonuniform grids, which is not confirmed by numerical experiments. We then present an analysis of the method which confirms that the solution error does indeed reduce as the cell size is reduced. This is supported by numerical calculations.

📜 SIMILAR VOLUMES

Formulations and analysis of the spectra
Formulations and analysis of the spectral volume method for the diffusion equation
✍ Sun, Yuzhi ;Wang, Z.J. 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 177 KB 👁 1 views

## Abstract The spectral volume (SV) method is a newly developed high‐order finite volume method for hyperbolic conservation laws on unstructured grids. It has been successfully demonstrated for multi‐dimensional Euler equations. We wish to extend the SV method to the Navier–Stokes equations. As a

A new finite volume method for the solut
A new finite volume method for the solution of convection-diffusion equations: analysis of stability and convergence
✍ Cordero, E. ;De Biase, L. ;Pennati, V. 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 246 KB 👁 3 views

A new high order FV method is presented for the solution of convection±diusion equations, based on a 4-point approximation of the diusive term and on the de®nition of a quadratic pro®le for the approximation of the convective term, in which coecients are obtained by imposing conditions on the trunca

Theoretical analysis of the Exponential
Theoretical analysis of the Exponential Transversal Method of Lines for the diffusion equation
✍ A. J. Salazar; M. Raydan; A. Campo 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 375 KB 👁 2 views

A new approximate technique to solve the diffusion equation, called the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation of the dependent variable to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide

The scaled boundary finite element metho
The scaled boundary finite element method—alias consistent infinitesimal finite element cell method—for diffusion
✍ Chongmin Song; John P. Wolf 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 194 KB 👁 2 views

The scaled boundary ÿnite element method, alias the consistent inÿnitesimal ÿnite element cell method, is developed starting from the di usion equation. Only the boundary of the medium is discretized with surface ÿnite elements yielding a reduction of the spatial dimension by one. No fundamental sol