@article{M2AN_2000__34_6_1123_0,
author = {Coudi\`ere, Yves and Villedieu, Philippe},
title = {Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1123--1149},
publisher = {Dunod},
volume = {34},
number = {6},
year = {2000},
mrnumber = {1812729},
zbl = {0972.65081},
language = {en},
url = {https://www.numdam.org/item/M2AN_2000__34_6_1123_0/}
}
TY - JOUR AU - Coudière, Yves AU - Villedieu, Philippe TI - Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2000 SP - 1123 EP - 1149 VL - 34 IS - 6 PB - Dunod UR - https://www.numdam.org/item/M2AN_2000__34_6_1123_0/ LA - en ID - M2AN_2000__34_6_1123_0 ER -
%0 Journal Article %A Coudière, Yves %A Villedieu, Philippe %T Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes %J ESAIM: Modélisation mathématique et analyse numérique %D 2000 %P 1123-1149 %V 34 %N 6 %I Dunod %U https://www.numdam.org/item/M2AN_2000__34_6_1123_0/ %G en %F M2AN_2000__34_6_1123_0
Coudière, Yves; Villedieu, Philippe. Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes. ESAIM: Modélisation mathématique et analyse numérique, Volume 34 (2000) no. 6, pp. 1123-1149. https://www.numdam.org/item/M2AN_2000__34_6_1123_0/
[1] and , Some error estimates for the box method. SIAM J. Numer. Anal. 24 (1987) 777 787. | Zbl | MR
[2] , and , Connection between finite volume and mixed finite element methods. RAIRO Modél. Math. Anal. Numér. 30 (1996) 445-465. | Zbl | MR | Numdam
[3] and , Local adaptative mesh refinement for shock hydrodynamics. J. Comput. Phys. 82 (1989) 64-84. | Zbl
[4] , On the finite volume element method. Numer. Math. 58 (1991) 713-735. | Zbl | MR
[5] , and , The finite volume element method for diffusion equations on general triangulations. SIAM J. Numer. Anal. 28 (1991) 392-402. | Zbl | MR
[6] and , On the accuracy of the finite volume element method for diffusion equations on composite grids. SIAM J. Numer. Anal 27 (1990) 636-655. | Zbl | MR
[7] , An Adaptatively-Refined, Cartesian, Cell-based Scheme for the Euler and Navier-Stokes Equations. Ph.D. thesis, Michigan Univ., NASA Lewis Research Center (1994).
[8] and , A Cartesian, cell-based approach for adaptative-refined solutions of the Euler and Navier-Stokes equations. AIAA (1995).
[9] , Analyse de schémas volumes finis sur maillages non structurés pour des problèmes linéaires hyperboliques et elliptiques. Ph.D. thesis, Université Paul Sabatier (1999).
[10] , and , Discrete sobolev inequalities and lp error estimates for approximate finite volume solutions of convection diffusion equation. Preprint of LATP, University of Marseille 1, 98-13 (1998).
[11] , and , Convergence rate of a finite volume scheme for a two dimensionnal diffusion convection problem. ESAIM: M2AN 33 (1999) 493-516. | Zbl | MR | Numdam
[12] and , Finite volume box schemes on triangular meshes. RAIRO Modél. Math. Anal. Numér. 32 (1998) 631-649. | Zbl | MR | Numdam
[13] , Elliptic Boundary Value Problems in Corner Domains. Lect. Notes Math., Springer-Verlag, Berlin (1988). | Zbl | MR
[14] , and , Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis. Math. Comp. 56 (1991) 437-461. | Zbl | MR
[15] , and , Finite volume methods, in Handbook of Numerical Analysis, P.G. Ciarlet and J.L. Lions Eds. (to appear). Prépublication No 97-19 du LATP, UMR 6632, Marseille (1997). | Zbl | MR
[16] and , Quadratic convergence for cell-centered grids. Appl Numer. Math. 4 (1988) 377-394. | Zbl | MR
[17] , Finite Difference Methods on Irregular Networks. Internat. Ser. Numer. Anal. 82, Birkhaüser, Verlag Basel (1987). | Zbl | MR
[18] , An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Numer. Methods Partial Differential Equations 11 (1994) 165-173. | Zbl | MR
[19] and , A Navier-Stokes algorithm for turbulent flows using an unstructured grid and flux difference splitting. AIAA (1994).
[20] and , On the finite volume element method for general self-adjoint elliptic problem. SIAM J. Numer. Anal. 35 (1998) 1762-1774. | Zbl | MR
[21] , Sur la résolution des systèmes hyperboliques du premier ordre par des méthodes d'éléments finis. Technical report, CEA (1976).
[22] and , The numerical solution of second-order boundary values problems on nonuniform meshes. Math. Comp. 47 (1986) 511-535. | Zbl | MR
[23] , Variational analysis of a mixed finite element finite volume scheme on general triangulations. Technical Report 2213, INRIA, Sophia Antipolis (1994).
[24] , Finite volume methods on voronoï meshes. Numer. Methods Partial Differential Equations 14 (1998) 193-212. | Zbl | MR
[25] and , Finite volume methods and their analysis. IMA J. Numer. Anal. 11 (1991) 241-260. | Zbl | MR
[26] , Convergence of finite volume schemes for Poisson's equation on nonuniform meshes. SIAM J. Numer. Anal. 28 (1991) 1419-1430. | Zbl | MR
[27] and . Analysis of finite volumes methods. Technical Report 95/19, CNRS, URA 1204 (1995).
[28] and , Convergence of finite volumes methods. Technical Report 95/20, CNRS, URA 1204 (1995).
[29] and , Convergence analysis of a finite volume method via a new nonconforming finite element method. Numer. Methods Partial Differential Equations 14 (1998) 213-231. | Zbl | MR
[30] , and . Finite difference schemes on triangular cell-centered grids with local refinement. SIAM J. Sci. Stat. Comput. 13 (1992) 1287-1313. | Zbl | MR
[31] and , On convergence of block-centered finite differences for elliptic problems. SIAM J. Numer. Anal. 25 (1988) 351-375. | Zbl | MR






