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

M. H. Vignal

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1996)

  • Volume: 30, Issue: 7, page 841-872
  • ISSN: 0764-583X

How to cite

top

Vignal, M. H.. "Convergence of a finite volume scheme for an elliptic-hyperbolic system." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 30.7 (1996): 841-872. <http://eudml.org/doc/193826>.

@article{Vignal1996,
author = {Vignal, M. H.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {elliptic-hyperbolic system; diphasic flow in a porous medium; finite volume scheme; error estimates; stability; convergence},
language = {eng},
number = {7},
pages = {841-872},
publisher = {Dunod},
title = {Convergence of a finite volume scheme for an elliptic-hyperbolic system},
url = {http://eudml.org/doc/193826},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Vignal, M. H.
TI - Convergence of a finite volume scheme for an elliptic-hyperbolic system
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1996
PB - Dunod
VL - 30
IS - 7
SP - 841
EP - 872
LA - eng
KW - elliptic-hyperbolic system; diphasic flow in a porous medium; finite volume scheme; error estimates; stability; convergence
UR - http://eudml.org/doc/193826
ER -

References

top
  1. [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. Zbl0865.35082MR1335655
  2. [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. Zbl0801.65089MR1245008
  3. [3] R. DIPERNA, 1985, Measure-Valued Solutions to Conservation Laws, Arch. Rat. Mech. Anal., 88, pp. 223-270. Zbl0616.35055MR775191
  4. [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. Zbl0981.65095
  5. [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. Zbl0792.65073MR1249455
  6. [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. 
  7. [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. Zbl0806.35114MR1235201
  8. [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. Zbl0822.65085MR1316144
  9. [9] R. HERBIN, O. LABERGERIE, Finite volume and finite element schemes for elliptic-hyperbolic problems, submitted. Zbl0897.76072
  10. [10] A. SZEPESSY, 1989, Measure valued solution of scalar conservation laws with boundary conditions, Arch. Rat. Mech. Anal., 107, 2, pp. 182-193. Zbl0702.35155MR996910
  11. [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. Zbl0813.65115MR1185647

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.