J. Droniou and J. Raymond, Optimal pointwise control of semilinear parabolic equations, Theory Methods, pp.135-156, 2000.
DOI : 10.1016/S0362-546X(98)00170-9

J. Droniou, A. Porretta, and A. Prignet, Parabolic capacity and soft measures for nonlinear equations, Potential Analysis, vol.19, issue.2, pp.99-161, 2003.
DOI : 10.1023/A:1023248531928

?. , J. Droniou, and T. Gallouët, Finite volume methods for convection-diffusion equations with right-hand side in H, M2AN Math. Model. Numer. Anal, vol.36, issue.4, pp.705-724, 2002.

J. Droniou, T. Gallouët, and J. Vovelle, Global solution and smoothing effect for a non-local regularization of a hyperbolic equation, Journal of Evolution Equations, vol.3, issue.3, pp.499-521, 2003.
DOI : 10.1007/s00028-003-0503-1
URL : https://hal.archives-ouvertes.fr/hal-00003438

C. Bacuta, J. Bramble, and J. Pasciak, New interpolation results and applications to finite element methods for elliptic boundary value problems, Journal of Numerical Mathematics, vol.9, issue.3, pp.179-198, 2001.
DOI : 10.1515/JNMA.2001.179
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.2119

C. Bardos, A. Y. Le-roux, and J. Nédélec, First order quasilinear equations with boundary conditions, Communications in Partial Differential Equations, vol.2, issue.33, pp.1017-1034, 1979.
DOI : 10.1090/S0025-5718-1977-0478651-3

P. Benilan, L. Boccardo, T. Gallouët, R. Gariepy, M. Pierre et al., An L 1 - Theory of Existence and Uniqueness of Solutions of Nonlinear Elliptic Equations, Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat., IV, issue.2, pp.22-241, 1995.

P. Bénilan, H. Brezis, and M. G. Crandall, A semilinear equation in L 1, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.2, pp.523-555, 1975.

J. Bergh and J. Löfström, Interpolation Spaces, 1976.
DOI : 10.1007/978-3-642-66451-9

P. Biler, T. Funaki, and W. A. Woyczynski, Fractal Burgers Equations, Journal of Differential Equations, vol.148, issue.1, pp.9-46, 1998.
DOI : 10.1006/jdeq.1998.3458
URL : http://doi.org/10.1006/jdeq.1998.3458

P. Biler, G. Karch, and W. A. Woyczynski, Asymptotics for conservation laws involving L??vy diffusion generators, Studia Mathematica, vol.148, issue.2, pp.171-192, 2001.
DOI : 10.4064/sm148-2-5

P. Biler, G. Karch, and W. A. Woyczynski, Asymptotics for multifractal conservation laws, Studia Math, vol.135, issue.3, pp.231-252, 1999.
DOI : 10.1016/s0764-4442(00)00187-7

L. Boccardo, Problemi differenziali ellittici e parabolici con dati misure, Boll. Un. Mat. Ital. A, vol.11, issue.7 2, pp.439-461, 1997.

L. Boccardo and T. Gallouët, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal, vol.87, pp.241-273, 1989.
DOI : 10.1016/0022-1236(89)90005-0
URL : http://doi.org/10.1016/0022-1236(89)90005-0

L. Boccardo and T. Gallouët, Nonlinear Elliptic Equations with Right Hand Side Measures, Communications in Partial Differential Equations, vol.15, issue.3-4, pp.641-655, 1992.
DOI : 10.1007/BF01766148

L. Boccardo, T. Gallouët, and L. Orsina, Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.13, issue.5, pp.539-551, 1996.
DOI : 10.1016/S0294-1449(16)30113-5

L. Boccardo, T. Gallouët, and J. Vazquez, Nonlinear Elliptic Equations in RN without Growth Restrictions on the Data, Journal of Differential Equations, vol.105, issue.2, pp.334-363, 1993.
DOI : 10.1006/jdeq.1993.1092

S. Boivin, F. Cayré, and J. M. Hérard, A finite volume method to solve the Navier???Stokes equations for incompressible flows on unstructured meshes, International Journal of Thermal Sciences, vol.39, issue.8, pp.806-825, 2000.
DOI : 10.1016/S1290-0729(00)00276-3

J. Bony, P. Courrège, and P. Priouret, Semi-groupes de Feller sur une vari??t?? ?? bord compacte et probl??mes aux limites int??gro-diff??rentiels du second ordre donnant lieu au principe du maximum, Annales de l???institut Fourier, vol.18, issue.2, pp.369-521, 1968.
DOI : 10.5802/aif.306
URL : http://archive.numdam.org/article/AIF_1968__18_2_369_0.pdf

J. Bramble, Interpolation between Sobolev spaces in Lipschitz domains with an application to multigrid theory, Mathematics of Computation, vol.64, issue.212, pp.1359-1365, 1995.
DOI : 10.1090/S0025-5718-1995-1308447-2

J. Bramble and S. Hilbert, Bounds for a class of linear functionals with applications to Hermite interpolation, Numerische Mathematik, vol.67, issue.4, pp.362-369, 1974.
DOI : 10.1007/BF02165007

H. Brezis and W. Strauss, Semi-linear second-order elliptic equations in $L^{1}$, Journal of the Mathematical Society of Japan, vol.25, issue.4, pp.565-590, 1973.
DOI : 10.2969/jmsj/02540565

C. Chainais-hillairet and E. Grenier, Numerical boundary layers for hyperbolic systems in 1-D, ESAIM: Mathematical Modelling and Numerical Analysis, vol.35, issue.1, pp.91-106, 2001.
DOI : 10.1051/m2an:2001100

P. Chatzipantelidis and R. D. Lazarov, The finite volume element method in nonconvex polygonal domains. Finite Volumes for Complex Applications III, Hermes Penton Science, pp.171-178, 2002.

S. H. Chou and P. S. Vassilevski, A general mixed covolume framework for constructing conservative schemes for elliptic problems, Mathematics of Computation, vol.68, issue.227, pp.991-1011, 1999.
DOI : 10.1090/S0025-5718-99-01090-X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.2094

P. Clavin and B. Denet, Theory of cellular detonations in gases. Part??2. Mach-stem formation at strong overdrive, no. Série II b, pp.489-496, 2001.
DOI : 10.1016/S1620-7742(01)01352-6

P. Clavin and B. Denet, Diamond Patterns in the Cellular Front of an Overdriven Detonation, Physical Review Letters, vol.88, issue.4, 2002.
DOI : 10.1103/PhysRevLett.88.044502

P. Clavin and L. He, Theory of cellular detonations in gases. Part??1. Stability limits at strong overdrive, no. Série II b, pp.463-471, 2001.
DOI : 10.1016/S1620-7742(01)01351-4

Y. Coudì-ere, T. Gallouët, and R. Herbin, error estimates for finite volume solutions of convection diffusion equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.35, issue.4, pp.767-778, 2001.
DOI : 10.1051/m2an:2001135

Y. Coudì-ere, J. P. Vila, and P. Villedieu, Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.3, pp.493-516, 1999.
DOI : 10.1051/m2an:1999149

D. Maso, G. Murat, F. Orsina, L. Prignet, and A. , Renormalized solutions for elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.28, issue.4, pp.741-808, 1999.

A. Dall-'aglio, Approximated solutions of equations withL 1 data. Application to theH-convergence of quasi-linear parabolic equations, Annali di Matematica Pura ed Applicata, vol.361, issue.1, pp.207-240, 1996.
DOI : 10.1007/BF01758989

R. J. Diperna, Measure-valued solutions to conservation laws, Archive for Rational Mechanics and Analysis, vol.2, issue.3, pp.223-270, 1985.
DOI : 10.1007/BF00752112

J. Droniou, Non Coercive Linear Elliptic Problems. Potential Anal, pp.181-203, 2002.

J. Droniou and T. Gallouët, A finite volume scheme for noncoercive Dirichlet problems with righthand side in H ?1 . Finite volume for complex applications III, Hermes Penton Science, pp.195-202, 2002.

J. Droniou and T. Gallouët, A uniqueness result for quasilinear elliptic equations with measures as data, Rend. Mat. Appl, vol.21, issue.7 14, pp.57-86, 2001.

J. Droniou, T. Gallouët, and R. Herbin, A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data, SIAM Journal on Numerical Analysis, vol.41, issue.6, 1997.
DOI : 10.1137/S0036142902405205
URL : https://hal.archives-ouvertes.fr/hal-00003440

R. Eymard, T. Gallouët, and R. Herbin, Finite Volume Methods. Handbook of Numerical Analysis, pp.713-1020
URL : https://hal.archives-ouvertes.fr/hal-00346077

R. Eymard, T. Gallouët, and R. Herbin, Convergence of finite volume schemes for semilinear convection diffusion equations, Numerische Mathematik, vol.82, issue.1, pp.91-116, 1999.
DOI : 10.1007/s002110050412

R. Eymard, T. Gallouët, and R. Herbin, Finite volume approximation of elliptic problems and convergence of an approximate gradient, Applied Numerical Mathematics, vol.37, issue.1-2, pp.31-53, 2001.
DOI : 10.1016/S0168-9274(00)00024-6

R. Eymard, T. Gallouët, R. Herbin, and A. Michel, Convergence of a finite volume scheme for nonlinear degenerate parabolic equations, Numerische Mathematik, vol.92, issue.1, pp.41-82, 2002.
DOI : 10.1007/s002110100342

P. Fabrie and T. Gallouët, MODELING WELLS IN POROUS MEDIA FLOW, Mathematical Models and Methods in Applied Sciences, vol.10, issue.05, pp.673-709, 2000.
DOI : 10.1142/S0218202500000367

W. Farkas, N. Jacob, and R. L. Schilling, Feller semigroups, Lp -sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols, Forum Mathematicum, vol.13, issue.1, pp.51-90, 2001.
DOI : 10.1515/FORM.2001.51
URL : https://epub.ub.uni-muenchen.de/17872/1/form.2001.51.pdf

J. M. Fiard and R. Herbin, Comparison between finite volume and finite element methods for an elliptic system arising in electrochemical engineering, Computer Methods in Applied Mechanics and Engineering, vol.115, issue.3-4, pp.315-338, 1994.
DOI : 10.1016/0045-7825(94)90065-5

P. A. Forsyth and P. H. Sammon, Quadratic convergence for cell-centered grids, Applied Numerical Mathematics, vol.4, issue.5, pp.377-394, 1988.
DOI : 10.1016/0168-9274(88)90016-5

T. Gallouët and R. Herbin, Finite volume methods for diffusion problems and irregular data. Finite volumes for complex applications, Problems and Perspectives, II, pp.155-162, 1999.

T. Gallouët and R. Herbin, Convergence of linear finite elements for diffusion equations with measure data, Comptes Rendus Mathematique, vol.338, issue.1, pp.81-84, 2004.
DOI : 10.1016/j.crma.2003.11.024

T. Gallouët, R. Herbin, and M. H. Vignal, Error estimate for the approximate finite volume solutions of convection diffusion equations with Dirichlet, Neumann or Fourier boundary conditions

T. Gallouët and A. Monier, On the regularity of solutions to elliptic equations, Rend. Mat., VII, vol.19, pp.471-488, 1999.

M. Gisclon and D. Serre, Conditions aux limites pour un syst??me strictement hyperbolique fournies, par le sch??ma de Godunov, ESAIM: Mathematical Modelling and Numerical Analysis, vol.31, issue.3, pp.31-359, 1997.
DOI : 10.1051/m2an/1997310303591
URL : http://archive.numdam.org/article/M2AN_1997__31_3_359_0.pdf

E. Grenier and O. Gù-es, Boundary Layers for Viscous Perturbations of Noncharacteristic Quasilinear Hyperbolic Problems, Journal of Differential Equations, vol.143, issue.1, pp.110-146, 1998.
DOI : 10.1006/jdeq.1997.3364

P. Grisvard, Elliptic problems in nonsmooth domains, 1985.
DOI : 10.1137/1.9781611972030

O. Gù, Perturbations visqueuses deprobì emes mixtes hyperboliques et couches limites, Ann. Inst. Fourier (Grenoble), vol.45, pp.973-1006, 1995.

O. Guibe, B. Cheikh, and M. , Résultats d'existence et d'unicité pour une classe deprobì emes non linéaires et non coercitifs, C. R. Acad. Sci. Paris Sér. I Math, vol.329, issue.11, pp.967-972, 1999.

R. Herbin, An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh, Numerical Methods for Partial Differential Equations, vol.28, issue.2, pp.165-173, 1995.
DOI : 10.1002/num.1690110205

R. Herbin, Finite volume approximation of elliptic problems with irregular data. Finite volumes for complex applications, Problems and Perspectives, Hermes, pp.153-160, 1999.

W. Hoh, Pseudodifferential operators with negative definite symbols and the martingale problem, Stochastics Stochastics Rep, vol.55, issue.3-4, pp.225-252, 1995.

C. Imbert and J. Vovelle, A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications. To appear in " SIAM -Mathematical Analysis
URL : https://hal.archives-ouvertes.fr/hal-00176541

K. T. Joseph and P. G. Lefloch, Boundary Layers in Weak Solutions of Hyperbolic Conservation Laws, Archive for Rational Mechanics and Analysis, vol.147, issue.1, pp.47-88, 1999.
DOI : 10.1007/s002050050145

S. N. Kru?kov, FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES, Mathematics of the USSR-Sbornik, vol.10, issue.2, pp.228-255, 1970.
DOI : 10.1070/SM1970v010n02ABEH002156

N. N. Kuznecov, The accuracy of certain approximate methods for the computation of weak solutions of a first order quasilinear equation, Z. Vy?isl. Mat. i Mat. Fiz, vol.16, pp.1489-1502, 1627.

O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Ural?eva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, vol.23, 1967.

R. D. Lazarov, I. D. Mishev, and P. S. Vassilevski, Finite Volume Methods for Convection-Diffusion Problems, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.31-55, 1996.
DOI : 10.1137/0733003
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.6889

J. Leray and J. L. Lions, Quelques résultats de Vi?ik sur lesprobì emes elliptiques semi-linéaires par les méthodes de Minty et Browder, Bull. Soc. Math. France, vol.93, pp.97-107, 1965.
DOI : 10.1007/978-3-642-11030-6_1
URL : http://archive.numdam.org/article/SJL_1964___1_1_0.pdf

P. Lévy, Calcul des Probabilités, 1925.

J. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, 1972.
DOI : 10.1007/978-3-642-65161-8

P. Lions, B. Perthame, and E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations, Journal of the American Mathematical Society, vol.7, issue.1, pp.169-191, 1994.
DOI : 10.1090/S0894-0347-1994-1201239-3

T. A. Manteufel and A. B. White, The numerical solution of second-order boundary value problems on nonuniform meshes, Mathematics of Computation, vol.47, issue.176, pp.511-535, 1986.
DOI : 10.1090/S0025-5718-1986-0856700-3

N. G. Meyers, An L p estimate for the gradient of solutions of second order divergence equations, Ann. Sc. Norm. Sup. Pisa, vol.17, pp.189-206, 1963.

I. Mishev, Finite volume element methods for non-definite problems, Numerische Mathematik, vol.83, issue.1, pp.161-175, 1999.
DOI : 10.1007/s002110050443
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.2183

I. D. Mishev, Finite volume methods on Voronoi meshes, Numerical Methods for Partial Differential Equations, vol.33, issue.2, pp.193-212, 1998.
DOI : 10.1002/(SICI)1098-2426(199803)14:2<193::AID-NUM4>3.0.CO;2-J
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.5340

J. Ne?as, Les méthodes directes en théorie deséquationsdeséquations elliptiques, 1967.

F. Otto, Initial-boundary value problem for a scalar conservation law, C. R. Acad. Sci. Paris Sér. I Math, vol.322, pp.729-734, 1996.

B. Perthame, Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure, Journal de Math??matiques Pures et Appliqu??es, vol.77, issue.10, pp.1055-1064, 1998.
DOI : 10.1016/S0021-7824(99)80003-8

M. Pierre, Parabolic Capacity and Sobolev Spaces, SIAM Journal on Mathematical Analysis, vol.14, issue.3, pp.522-533, 1983.
DOI : 10.1137/0514044
URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA093570

A. Prignet, Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat. Appl, vol.15, issue.7 3, pp.321-337, 1995.

G. Stampacchia, Leprobì eme de Dirichlet pour leséquationsleséquations elliptiques du second ordrè a coefficients discontinus, pp.15-189, 1965.

E. Tadmor and T. Tang, Pointwise Error Estimates for Relaxation Approximations to Conservation Laws, SIAM Journal on Mathematical Analysis, vol.32, issue.4, pp.870-886, 2000.
DOI : 10.1137/S0036141098349492

T. Tang, Error estimates of approximate solutions for nonlinear scalar conservation laws Hyperbolic problems: theory, numerics, applications, Internat. Ser. Numer. Math, vol.141, issue.140, pp.873-882, 2000.

A. I. Vol, Spaces bv and quasilinear equations, Mat. Sb. (N.S.), vol.73, issue.115, pp.255-302, 1967.

W. Woyczy´nskiwoyczy´nski, Lévy processes in the physical sciences. Lévy processes, pp.241-266, 2001.