Convergence of a finite volume scheme for an elliptic-hyperbolic system

M. H. Vignal

doi:10.1051/m2an/1996300708411

All issues

Volume 30 / No 7 (1996)

ESAIM: M2AN, 30 7 (1996) 841-872

References

Free Access

Issue		ESAIM: M2AN Volume 30, Number 7, 1996


Page(s)		841 - 872
DOI		https://doi.org/10.1051/m2an/1996300708411
Published online		31 January 2017

S. BENHARBIT, A. CHALABI, J. P. VILA, Numerical Viscosity and Convergence of Finite Volume Methods for Conservation Laws with Boundary Conditions, to appear in SIAM Journal of Num. Anal. [MR: 1335655] [Zbl: 0865.35082] [Google Scholar]
S. CHAMPIER, T. GALLOUET, R. HERBIN, 1993, Convergence of an Upstream finite volume scheme on a Triangular Mesh for a Nonlinear Hyperbolic Equation, Numer. Math. 66, pp. 139-157. [EuDML: 133756] [MR: 1245008] [Zbl: 0801.65089] [Google Scholar]
R. DIPERNA, 1985, Measure-Valued Solutions to Conservation Laws, Arch. Rat. Mech. Anal., 88, pp. 223-270. [MR: 775191] [Zbl: 0616.35055] [Google Scholar]
R. EYMARD, T. GALLOUET, R. HERBIN, The finite volume method, in preparation for the Handbook of Numerical Analysis Ph. Ciarlet and J. L. Lions eds. [Zbl: 0981.65095] [Google Scholar]
R. EYMARD, T. GALLOUET, 1993, Convergence d'un schéma de type Eléments Finis-Volumes Finis pour un système formé d'une équation elliptique et d'une équation hyperbolique, M2AN, 27, 7, pp. 843-861. [EuDML: 193726] [MR: 1249455] [Zbl: 0792.65073] [Google Scholar]
J. M. FIARD and R. HERBIN, 1994, Comparison between finite volume and finite element methods for the numerical computation of an elliptic problem arising in electrochemical engineering, Comput. Math. Appl. Mech. Engin., 115, pp. 315-338. [Google Scholar]
T. GALLOUET, R. HERBIN, 1993, A uniqueness Result for Measure Valued Solutions of Non Linear Hyperbolic Equations, Differential Integral Equations, 6, 6, pp. 1383-1394. [MR: 1235201] [Zbl: 0806.35114] [Google Scholar]
R. HERBIN, 1994, An error estimate for a finite volume scheme for a diffusion convection problem on a triangular mesh, Num. Meth. in P.D.E. [MR: 1316144] [Zbl: 0822.65085] [Google Scholar]
R. HERBIN, O. LABERGERIE, Finite volume and finite element schemes for elliptic-hyperbolic problems, submitted. [Zbl: 0897.76072] [Google Scholar]
A. SZEPESSY, 1989, Measure valued solution of scalar conservation laws with boundary conditions, Arch. Rat. Mech. Anal., 107, 2, pp. 182-193. [MR: 996910] [Zbl: 0702.35155] [Google Scholar]
P. S. VASSILEVSKI, S. I. PETROVA, R. D. LAZAROV, 1992, Finite Difference Schemes on Triangular Cell-Centered Grids With Local Refinement, SIAM J. Sci. Stat. Comput., 13, 6, pp. 1287-1313. [MR: 1185647] [Zbl: 0813.65115] [Google Scholar]

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[1] S. BENHARBIT, A. CHALABI, J. P. VILA, Numerical Viscosity and Convergence of Finite Volume Methods for Conservation Laws with Boundary Conditions, to appear in SIAM Journal of Num. Anal. [MR: 1335655] [Zbl: 0865.35082] [Google Scholar]

[2] S. CHAMPIER, T. GALLOUET, R. HERBIN, 1993, Convergence of an Upstream finite volume scheme on a Triangular Mesh for a Nonlinear Hyperbolic Equation, Numer. Math. 66, pp. 139-157. [EuDML: 133756] [MR: 1245008] [Zbl: 0801.65089] [Google Scholar]

[3] R. DIPERNA, 1985, Measure-Valued Solutions to Conservation Laws, Arch. Rat. Mech. Anal., 88, pp. 223-270. [MR: 775191] [Zbl: 0616.35055] [Google Scholar]

[4] R. EYMARD, T. GALLOUET, R. HERBIN, The finite volume method, in preparation for the Handbook of Numerical Analysis Ph. Ciarlet and J. L. Lions eds. [Zbl: 0981.65095] [Google Scholar]

[5] R. EYMARD, T. GALLOUET, 1993, Convergence d'un schéma de type Eléments Finis-Volumes Finis pour un système formé d'une équation elliptique et d'une équation hyperbolique, M2AN, 27, 7, pp. 843-861. [EuDML: 193726] [MR: 1249455] [Zbl: 0792.65073] [Google Scholar]

[6] J. M. FIARD and R. HERBIN, 1994, Comparison between finite volume and finite element methods for the numerical computation of an elliptic problem arising in electrochemical engineering, Comput. Math. Appl. Mech. Engin., 115, pp. 315-338. [Google Scholar]

[7] T. GALLOUET, R. HERBIN, 1993, A uniqueness Result for Measure Valued Solutions of Non Linear Hyperbolic Equations, Differential Integral Equations, 6, 6, pp. 1383-1394. [MR: 1235201] [Zbl: 0806.35114] [Google Scholar]

[8] R. HERBIN, 1994, An error estimate for a finite volume scheme for a diffusion convection problem on a triangular mesh, Num. Meth. in P.D.E. [MR: 1316144] [Zbl: 0822.65085] [Google Scholar]

[9] R. HERBIN, O. LABERGERIE, Finite volume and finite element schemes for elliptic-hyperbolic problems, submitted. [Zbl: 0897.76072] [Google Scholar]

[10] A. SZEPESSY, 1989, Measure valued solution of scalar conservation laws with boundary conditions, Arch. Rat. Mech. Anal., 107, 2, pp. 182-193. [MR: 996910] [Zbl: 0702.35155] [Google Scholar]

[11] P. S. VASSILEVSKI, S. I. PETROVA, R. D. LAZAROV, 1992, Finite Difference Schemes on Triangular Cell-Centered Grids With Local Refinement, SIAM J. Sci. Stat. Comput., 13, 6, pp. 1287-1313. [MR: 1185647] [Zbl: 0813.65115] [Google Scholar]