Solution of degenerate parabolic variational inequalities with convection

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1. [1] H.W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1983) 311–341. Zbl0497.35049
2. [2] H.W. Alt, S. Luckhaus and A. Visintin, On the nonstationary flow through porous media. Ann. Math. Pura Appl. CXXXVI (1984) 303–316. Zbl0552.76075
3. [3] J. Babušikova, Application of relaxation scheme to degenerate variational inequalities. Appl. Math. 46 (2001) 419–439. Zbl1061.49004
4. [4] J.W. Barrett and P. Knabner, Finite element approximation of transport of reactive solutes in porous media. II: Error estimates for equilibrium adsorption processes. SIAM J. Numer. Anal. 34 (1997) 455–479. Zbl0904.76039
5. [5] J.W. Barrett and P. Knabner, An improved error bound for a Lagrange-Galerkin method for contaminant transport with non-lipschitzian adsorption kinetics. SIAM J. Numer. Anal. 35 (1998) 1862–1882. Zbl0911.65078
6. [6] J. Bear, Dynamics of Fluid in Porous Media. Elsevier, New York (1972). Zbl1191.76001
7. [7] R. Bermejo, Analysis of an algorithm for the Galerkin-characteristics method. Numer. Math. 60 (1991) 163–194. Zbl0723.65073
8. [8] R. Bermejo, A Galerkin-characteristics algorithm for transport-diffusion equation. SIAM J. Numer. Anal. 32 (1995) 425–455. Zbl0854.65083
9. [9] C.N. Dawson, C.J. Van Duijn and M.F. Wheeler, Characteristic-Galerkin methods for contaminant transport with non-equilibrium adsorption kinetics. SIAM J. Numer. Anal. 31 (1994) 982–999. Zbl0808.76046
10. [10] R Douglas and T.F. Russel, Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. 19 (1982) 871–885. Zbl0492.65051
11. [11] R.E. Ewing and H. Wang, Eulerian-Lagrangian localized adjoint methods for linear advection or advection-reaction equations and their convergence analysis. Comput. Mech. 12 (1993) 97–121. Zbl0774.76058
12. [12] R. Eymard, M. Gutnic and D. Hilhorst, The finite volume method for Richards equation. Comput. Geosci. 3 (1999) 259–294. Zbl0953.76060
13. [13] P. Frolkovic, Flux-based method of characteristics for contaminant transport in flowing groundwater. Computing and Visualization in Science 5 (2002) 73–83. Zbl1052.76578
14. [14] R. Glowinski, J.-L. Lions and R. Tremolieres, Numerical analysis of variational inequalities, Vol. 8. North-Holland Publishing Company, Stud. Math. Appl. (1981). Zbl0463.65046MR635927
15. [15] A. Handlovicova, Solution of Stefan problems by fully discrete linear schemes. Acta Math. Univ. Comenianae (N.S.) 67 (1998) 351–372. Zbl0930.65108
16. [16] H. Holden, K.H. Karlsen and K.-A. Lie, Operator splitting methods for degenerate convection-diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation. Comput. Geosci. 4 (2000) 287–323. Zbl1049.35113
17. [17] W. Jäger and J. Kačur, Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes. Math. Modelling Numer. Anal. 29 (1995) 605–627. Zbl0837.65103
18. [18] J. Kačur, Solution of some free boundary problems by relaxation schemes. SIAM J. Numer. Anal. 36 (1999) 290–316. Zbl0924.65090
19. [19] J. Kačur, Solution to strongly nonlinear parabolic problems by a linear approximation scheme. IMA J. Numer. Anal. 19 (1999) 119–154. Zbl0946.65145
20. [20] J. Kačur, Solution of degenerate convection-diffusion problems by the method of characteristics. SIAM J. Numer. Anal. 39 (2001) 858–879. Zbl1011.65064
21. [21] J. Kačur and S. Luckhaus, Approximation of degenerate parabolic systems by nondegenerate alliptic and parabolic systems. Appl. Numer. Math. 25 (1997) 1–21. Zbl0894.65043
22. [22] J. Kačur and R. van Keer, Solution of contaminant transport with adsorption in porous media by the method of characteristics. ESAIM: M2AN 35 (2001) 981–1006. Zbl0995.76070
23. [23] A. Kufner, O. John and S. Fučík, Function spaces. Academia, Prague (1977). Zbl0364.46022MR482102
24. [24] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Vol. XX. Dunod, Gauthier-Villars, Paris (1969). Zbl0189.40603MR259693
25. [25] K. Mikula, Numerical solution of nonlinear diffusion with finite extinction phenomena. Acta Math. Univ. Comenian. (N.S.) 2 (1995) 223–292. Zbl0852.35080
26. [26] J. Nečas, Les méthodes directes en théorie des équations elliptiques. Academia, Prague (1967). MR227584
27. [27] F. Otto, L1 – contraction and uniqueness for quasilinear elliptic – parabolic equations. C. R. Acad. Sci Paris Sér. I Math. 321 (1995) 105–110. Zbl0845.35056
28. [28] P. Pironneau, On the transport-diffusion algorithm and its application to the Navier-Stokes equations. Numer. Math. 38 (1982) 309–332. Zbl0505.76100
29. [29] X. Shi, H. Wang and R.E. Ewing, An ellam scheme for multidimensional advection-reaction equations and its optimal-order error estimate. SIAM J. Numer. Anal. 38 (2001) 1846–1885. Zbl1006.76074