HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

A Finite Volume Scheme for Diffusion Problems on General Meshes Applying Monotony Constraints

Abstract : In order to increase the accuracy and the stability of a scheme dedicated to the approximation of diffusion operators on any type of grids, we propose a method which locally reduces the curvature of the discrete solution where the loss of monotony is observed. The discrete solution is shown to fulfill a variational formulation, thanks to the use of Lagrange multipliers. We can then show its convergence to the solution of the continuous problem, and an error estimate is derived. A numerical method, based on Uzawa's algorithm, is shown to provide accurate and stable approximate solutions to various problems. Numerical results show the increase of precision due to the application of the method.
Document type :
Journal articles
Complete list of metadata

Cited literature [17 references]  Display  Hide  Download

Contributor : Eric Chénier Connect in order to contact the contributor
Submitted on : Wednesday, April 25, 2012 - 6:02:48 PM
Last modification on : Saturday, January 15, 2022 - 4:16:36 AM
Long-term archiving on: : Monday, November 26, 2012 - 3:51:14 PM


Files produced by the author(s)




O. Angélini, C. Chavant, Eric Chénier, R. Eymard. A Finite Volume Scheme for Diffusion Problems on General Meshes Applying Monotony Constraints. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2010, 47 (6), pp.4193-4213. ⟨10.1137/080732183⟩. ⟨hal-00691261⟩



Record views


Files downloads