[1]
M. Afif and B. Amaziane, *Convergence of finite volume schemes for a degenerate convection-diffusion equation arising in two-phase flow in porous media*. Preprint (1999).

[2]
Bouchut, F., Guarguaglini, F.R. and Natalini, R., Diffusive BGK approximations for nonlinear multidimensional parabolic equations.
*Indiana Univ. Math. J.*
49 (2000) 723-749.

[3]
Bürger, R., Evje, S. and Karlsen, K.H., On strongly degenerate convection-diffusion problems modeling sedimentation-consolidation processes.
*J. Math. Anal. Appl.*
247 (2000) 517-556.

[4]
M.C. Bustos, F. Concha, R. Bürger and E.M. Tory, *Sedimentation and thickening: Phenomenological foundation and mathematical theory*. Kluwer Academic Publishers, Dordrecht (1999).

[5]
Carrillo, J., Entropy solutions for nonlinear degenerate problems.
*Arch. Rational Mech. Anal.*
147 (1999) 269-361.

[6]
Chainais-Hillairet, C., Finite volume schemes for a nonlinear hyperbolic equation. Convergence towards the entropy solution and error estimate.
*RAIRO-Modél. Math. Anal. Numér.*
33 (1999) 129-156.

[7]
Champier, S., Gallouët, T. and Herbin, R., Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh.
*Numer. Math.*
66 (1993) 139-157.

[8]
Cockburn, B., Coquel, F. and Le Floch, P., An error estimate for finite volume methods for multidimensional conservation laws.
*Math. Comp.*
63 (1994) 77-103.

[9]
Cockburn, B., Coquel, F. and LeFloch, P.G., Convergence of the finite volume method for multidimensional conservation laws.
*SIAM J. Numer. Anal.*
32 (1995) 687-705.

[10]
Cockburn, B. and Gremaud, P.-A., *A priori* error estimates for numerical methods for scalar conservation laws. I. The general approach.
*Math. Comp.*
65 (1996) 533-573.

[11]
Cockburn, B. and Shu, C.-W., The local discontinuous Galerkin method for time-dependent convection-diffusion systems.
*SIAM J. Numer. Anal.*
35 (1998) 2440-2463 (electronic).

[12]
Crandall, M.G. and Majda, A., Monotone difference approximations for scalar conservation laws.
*Math. Comp.*
34 (1980) 1-21.

[13]
Crandall, M.G. and Tartar, L., Some relations between nonexpansive and order preserving mappings.
*Proc. Amer. Math. Soc.*
78 (1980) 385-390.

[14]
Engquist, B. and Osher, S., One-sided difference approximations for nonlinear conservation laws.
*Math. Comp.*
36 (1981) 321-351.

[15]
M.S. Espedal and K.H. Karlsen, Numerical solution of reservoir flow models based on large time step operator splitting algorithms, in *Filtration in Porous media and industrial applications*. *Lect. Notes Math.*
**1734**, Springer, Berlin (2000) 9-77.

[16]
Evje, S. and Karlsen, K.H., Discrete approximations of *BV* solutions to doubly nonlinear degenerate parabolic equations.
*Numer. Math.*
86 (2000) 377-417.

[17]
S. Evje and K.H. Karlsen, Degenerate convection-diffusion equations and implicit monotone difference schemes, in *Hyperbolic problems: Theory, numerics, applications*, Vol. I (Zürich, 1998). Birkhäuser, Basel (1999) 285-294.

[18]
Evje, S. and Karlsen, K.H., Viscous splitting approximation of mixed hyperbolic-parabolic convection-diffusion equations.
*Numer. Math.*
83 (1999) 107-137.

[19]
Evje, S. and Karlsen, K.H., Monotone difference approximations of *BV* solutions to degenerate convection-diffusion equations.
*SIAM J. Numer. Anal.*
37 (2000) 1838-1860 (electronic).

[20]
S. Evje and K.H. Karlsen, *Second order difference schemes for degenerate convection-diffusion equations*. Preprint (in preparation).

[21]
Eymard, R., Gallouët, T., Ghilani, M. and Herbin, R., Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes.
*IMA J. Numer. Anal.*
18 (1998) 563-594.

[22]
Eymard, R., Gallouët, T., Hilhorst, D. and Naït Slimane, Y., Finite volumes and nonlinear diffusion equations.
*RAIRO-Modél. Math. Anal. Numér.*
32 (1998) 747-761.

[23]
Gimse, T. and Risebro, N.H., Solution of the Cauchy problem for a conservation law with a discontinuous flux function.
*SIAM J. Math. Anal.*
23 (1992) 635-648.

[24]
A. Harten, J.M. Hyman and P.D. Lax, On finite-difference approximations and entropy conditions for shocks. *Comm. Pure Appl. Math.*
**XXIX** (1976) 297-322.

[25]
H. Holden, K.H. Karlsen and K.-A. Lie, Operator splitting methods for degenerate convection-diffusion equations I: Convergence and entropy estimates, in *Stochastic processes, physics and geometry: New interplays. A volume in honor of Sergio Albeverio*. Amer. Math. Soc. (to appear).

[26]
H. Holden, K.H. Karlsen, K.-A. Lie and N.H. Risebro, *Operator splitting for nonlinear partial differential equations: An *
*L*
^{1}
* convergence theory*. Preprint (in preparation).

[27]
Isaacson, E. and Temple, B., Convergence of the 2 x 2 Godunov method for a general resonant nonlinear balance law.
*SIAM J. Appl. Math.*
55 (1995) 625-640.

[28]
K.H. Karlsen and N.H. Risebro, *On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients*. Preprint, Department of Mathematics, University of Bergen (2000).

[29]
C. Klingenberg and N.H. Risebro, Stability of a resonant system of conservation laws modeling polymer flow with gravitation. *J. Differential Equations* March (2000).

[30]
Klingenberg, C. and Risebro, N.H., Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior.
*Comm. Partial Differential Equations*
20 (1995) 1959-1990.

[31]
Kröner, D., Noelle, S. and Rokyta, M., Convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions.
*Numer. Math.*
71 (1995) 527-560.

[32]
Kröner, D. and Rokyta, M., Convergence of upwind finite volume schemes for scalar conservation laws in two dimensions.
*SIAM J. Numer. Anal.*
31 (1994) 324-343.

[33]
Kruzkov, S.N., Results on the nature of the continuity of solutions of parabolic equations, and certain applications thereof.
*Mat. Zametki*
6 (1969) 97-108.

[34]
Kruzkov, S.N., First order quasi-linear equations in several independent variables.
*Math. USSR Sbornik*
10 (1970) 217-243.

[35]
Kurganov, A. and Tadmor, E., New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations.
*J. Comput. Phys.*
160 (2000) 241-282.

[36]
Kuznetsov, N.N., Accuracy of some approximative methods for computing the weak solutions of a first-order quasi-linear equation.
*USSR Comput. Math. Math. Phys. Dokl.*
16 (1976) 105-119.

[37]
Lucier, B.J., Error bounds for the methods of Glimm, Godunov and LeVeque.
*SIAM J. Numer. Anal.*
22 (1985) 1074-1081.

[38]
Noelle, S., Convergence of higher order finite volume schemes on irregular grids.
*Adv. Comput. Math.*
3 (1995) 197-218.

[39]
M. Ohlberger, *A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations*. Preprint, Mathematische Fakultät, Albert-Ludwigs-Universität Freiburg (2000).

[40]
Oleĭnik, O.A., Discontinuous solutions of non-linear differential equations.
*Amer. Math. Soc Transl. Ser. 2*
26 (1963) 95-172.

[41]
Osher, S. and Tadmor, E., On the convergence of difference approximations to scalar conservation laws.
*Math. Comp.*
50 (1988) 19-51.

[42]
Rouvre, É. and Gagneux, G., Solution forte entropique de lois scalaires hyperboliques-paraboliques dégénérées.
*C. R. Acad. Sci. Paris Sér. I Math.*
329 (1999) 599-602.

[43]
A.A. Samarskii, V.A. Galaktionov, S.P. Kurdyumov and A.P. Mikhailov, *Blow-up in quasilinear parabolic equations*. Walter de Gruyter & Co., Berlin (1995). Translated from the 1987 Russian original by Michael Grinfeld and revised by the authors.

[44]
Sanders, R., On convergence of monotone finite difference schemes with variable spatial differencing.
*Math. Comp.*
40 (1983) 91-106.

[45]
Temple, B., Global solution of the Cauchy problem for a class of 2 x 2 nonstrictly hyperbolic conservation laws.
*Adv. in Appl. Math.*
3 (1982) 335-375.

[48]
Convergence, J.-P. Vila and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicit monotone schemes.
*RAIRO-Modél. Math. Anal. Numér.*
28 (1994) 267-295.

[49]
Vol'pert, A.I., The spaces BV and quasi-linear equations.
*Math. USSR Sbornik*
2 (1967) 225-267.

[50]
Vol'pert, A.I. and Hudjaev, S.I., Cauchy's problem for degenerate second order quasilinear parabolic equations.
*Math. USSR Sbornik*
7 (1969) 365-387.