The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.
Mots clés : finite volume methods, ${L^p}$ error estimates, unstructured meshes, convection-diffusion equations
@article{M2AN_2001__35_4_767_0,
author = {Coudi\`ere, Yves and Gallou\"et, Thierry and Herbin, Rapha\`ele},
title = {Discrete {Sobolev} inequalities and $L^p$ error estimates for finite volume solutions of convection diffusion equations},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {767--778},
publisher = {EDP-Sciences},
volume = {35},
number = {4},
year = {2001},
mrnumber = {1863279},
zbl = {0990.65122},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_4_767_0/}
}
TY - JOUR AU - Coudière, Yves AU - Gallouët, Thierry AU - Herbin, Raphaèle TI - Discrete Sobolev inequalities and $L^p$ error estimates for finite volume solutions of convection diffusion equations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 767 EP - 778 VL - 35 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_2001__35_4_767_0/ LA - en ID - M2AN_2001__35_4_767_0 ER -
%0 Journal Article %A Coudière, Yves %A Gallouët, Thierry %A Herbin, Raphaèle %T Discrete Sobolev inequalities and $L^p$ error estimates for finite volume solutions of convection diffusion equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 767-778 %V 35 %N 4 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_2001__35_4_767_0/ %G en %F M2AN_2001__35_4_767_0
Coudière, Yves; Gallouët, Thierry; Herbin, Raphaèle. Discrete Sobolev inequalities and $L^p$ error estimates for finite volume solutions of convection diffusion equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 4, pp. 767-778. http://www.numdam.org/item/M2AN_2001__35_4_767_0/
[1] and, Some error estimates for the box method. SIAM J. Numer. Anal. 24 (1987) 777-787. | Zbl
[2] , Modélisation tridimensionnelle de la genèse des bassins sédimentaires. Thesis, École Nationale Supérieure des Mines de Paris, France (1996).
[3] , On the finite volume element method. Numer. Math. 58 (1991) 713-735. | Zbl
[4] , and, The finite volume element method for diffusion equations on general triangulations. SIAM J. Numer. Anal. 28 (1991) 392-402. | Zbl
[5] and, A Cartesian, cell-based approach for adaptative-refined solutions of the Euler and Navier-Stokes equations. AIAA J. 0566 (1995).
[6] , Elliptic boundary value problems in corner domains. Lecture Notes in Math. 1341 Springer-Verlag, Berlin (1988). | MR | Zbl
[7] and, A finite volume scheme for the linear convection-diffusion equation on locally refined meshes, in7-th international colloquium on numerical analysis, Plovdiv, Bulgaria (1998).
[8] , and, Convergence of a finite volume scheme for a diffusion problem, in Finite volumes for complex applications, problems and perspectives, F. Benkhaldoun and R. Vilsmeier Eds., Hermès, Paris (1996) 161-168.
[9] , and, Convergence rate of a finite volume scheme for a two dimensional convection diffusion problem. ESAIM: M2AN 33 (1999) 493-516. | Numdam | Zbl
[10] and, Convergence of a finite volume scheme for a two dimensional diffusion convection equation on locally refined meshes. ESAIM: M2AN 34 (2000) 1109-1295. | Numdam | Zbl
[11] , and, Convergence of finite volume schemes for semilinear convection diffusion equations. Numerische Mathematik. 82 (1999) 91-116. | Zbl
[12] and, Convergence d'un schéma de type éléments finis-volumes finis pour un système couplé elliptique-hyperbolique. RAIRO Modél. Math. Anal. Numér. 27 (1993) 843-861. | Numdam | Zbl
[13] , and, The finite volume method, in Handbook of numerical analysis, P.G. Ciarlet and J.L. Lions, Eds., Elsevier Science BV, Amsterdam (2000) 715-1022. | Zbl
[14] , A control volume method to solve an elliptic equation on a 2D irregular meshing. Comput. Methods Appl. Mech. Engrg. 100 (1992) 275-290. | Zbl
[15] , A control volume finite element approach to NAPL groundwater contamination. SIAM J. Sci. Stat. Comput. 12 (1991) 1029-1057. | Zbl
[16] and, Quadratic convergence for cell-centered grids. Appl. Numer. Math. 4 (1988) 377-394. | Zbl
[17] , and, Error estimate for the approximate finite volume solutions of convection diffusion equations with Dirichlet, Neumann or Fourier boundary conditions. SIAM J. Numer. Anal. 37 (2000) 1035-1072. | Zbl
[18] , Finite difference methods on irregular networks. A generalized approach to second order elliptic problems. Internat. Ser. Numer. Math. 82, Birkhäuser-Verlag, Stuttgart (1987). | MR | Zbl
[19] , An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Numer. Methods. Partial Differ. Equations 11 (1995) 165-173. | Zbl
[20] , Finite volume methods for diffusion convection equations on general meshes, in Finite volumes for complex applications, problems and perspectives, F. Benkhaldoun and R. Vilsmeier, Eds., Hermès, Paris (1996) 153-160.
[21] and, A Navier-Stokes algorithm for turbulent flows using an unstructured grid and flux difference splitting. AIAA J. 2292 (1994).
[22] and, Finite volume methods for reaction diffusion problems, in Finite volumes for complex applications, problems and perspectives, F. Benkhaldoun and R. Vilsmeier, Eds., Hermès, Paris (1996) 233-240 .
[23] , and, Finite volume methods for convection-diffusion problems. SIAM J. Numer. Anal. 33 (1996) 31-55. | Zbl
[24] and, The numerical solution of second order boundary value problem on non uniform meshes. Math. Comput. 47 (1986) 511-536. | Zbl
[25] and, Finite volume methods and their analysis. IMA J. Numer. Anal. 11 (1991) 241-260. | Zbl
[26] , Couplage espace-temps de schémas numériques en simulation de réservoir. Ph.D. Thesis, University of Pau, France (1994).
[27] , and, Finite difference schemes on triangular cell-centered grids with local refinement. SIAM J. Sci. Statist. Comput. 13 (1992) 1287-1313. | Zbl
