Monotone and conservative difference schemes for elliptic equations with mixed derivatives;Monotoniškos ir konservatyvios baigtinių skirtumų schemos eliptinio tipo lygtims su mišriomis išvestinemis

Mathematical Modelling and Analysis

Volumn 9, Issue 2, 2004, Pages 169-178

  Rybak, I V ^a  

^a INSTITUTE OF MATHEMATICS   (Belarus)

Author keywords

Conservative difference scheme; Elliptic equations; Grid maximum principle; Mixed derivatives; Monotone difference scheme

Indexed keywords

A-PRIORI ESTIMATES; CONSERVATIVE DIFFERENCE SCHEMES; DIFFERENCE SCHEMES; ELLIPTIC EQUATIONS; MIXED DERIVATIVES; SECOND ORDERS; STABILITY AND CONVERGENCE;

MAXIMUM PRINCIPLE;

EID: 33646543913     PISSN: 13926292     EISSN: 16483510     Source Type: Journal    
DOI: 10.1080/13926292.2004.9637250     Document Type: Article

References (11)

1. T. Arbogast, M. F. Wheeler and I. Yotov. Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. SIAM J. Numer. Anal., 34(2), 828-852, 1997.
2. P. Crumpton, G. Shaw and A. Ware. Discretization and multigrid solution of elliptic equations with mixed derivative terms and strongly discontinuous coefficients. J. Com-put. Phys., 116, 343-358, 1995.
3. S. Godunov and V. Ryabenkii. Difference schemes. Nauka, Moskow, 1973. (in Russian).
4. J. Hyman, J. Morel, M. Shashkov and S. Steinberg. Mimetic finite difference methods for diffusion equations. Computational Geosciences, 6, 333-352, 2002.
5. A. Samarskii. The theory of difference schemes. Marcel Dekker, Inc., New York-Basel, 2001.
6. A. Samarskii and V. Andreev. Difference methods for elliptic equations. Nauka, Moskow, 1976. (in Russian).
7. A. Samarskii, P. Matus, V. Mazhukin and I. Mozolevski. Monotone difference schemes for equations with mixed derivatives. Computers and Mathematics with Applications, 44, 501-510, 2002.
8. A. Samarskii, V. Mazhukin, P. Matus and G. Shishkin. Monotone difference schemes for equations with mixed derivatives. Mathematical Modeling, 13(2), 17-26, 2001.
9. G. Schneider and M. Zedan. A modified strongly implicit procedure for the numerical solution of field problems. Numerical Heat Transfer, 4, 1-19, 1981.
10. G. Shishkin. Grid approximation of the singularly perturbed boundary-value problem for quasilinear parabolic equations in the case of total degeneracy with respect to space variables. In: Yu. A. Kuznetsov(Ed.), Numerical methods and mathematical modeling, Russian Academy of Sciences, Institute of Computational Mathematics, Moskow, 103-128, 1992.
11. W. Voligt. Finite-difference schemes for parabolic problems with first and mixed second derivatives. Z. angew. Math, und Mech., 68(7), 281-288, 1988.