The discrete maximum principle for linear simplicial finite element approximations of a reaction-diffusion problem

Linear Algebra and Its Applications

Volumn 429, Issue 10, 2008, Pages 2344-2357

  Brandts, Jan H ^a   Korotov, Sergey ^a   Křížek, Michal ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Angle condition; Discrete maximum principle; Finite element method; Maximum principle; Reaction diffusion problem; Simplicial partition; Stieltjes matrix

Indexed keywords

ARSENIC COMPOUNDS; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION IN LIQUIDS; SEMICONDUCTOR DOPING;

ANGLE CONDITION; DISCRETE MAXIMUM PRINCIPLE; MAXIMUM PRINCIPLE; REACTION-DIFFUSION PROBLEM; SIMPLICIAL PARTITION; STIELTJES MATRIX;

FINITE ELEMENT METHOD;

EID: 51349142133     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.06.011     Document Type: Article

References (20)

1. Bouchon F. Monotonicity of some perturbations of irreducibly diagonally dominant M-matrices. Numer. Math. 105 (2007) 591-601
2. Bramble J.H., Hubbard B.E., and Thomée V. Convergence estimates for essentially positive type discrete problems. Math. Comput. 23 (1969) 695-710
3. n into n path-subsimplices. Linear Algebra Appl. 421 (2007) 382-393
4. Ciarlet P.G. Discrete maximum principle for finite-difference operators. Aequationes Math. 4 (1970) 338-352
5. Ciarlet P.G. The Finite Element Method for Elliptic Problems (1978), North-Holland, Amsterdam
6. Ciarlet P.G., and Raviart P.-A. Maximum principle and uniform convergence for the finite element method. Comput. Methods Appl. Mech. Eng. 2 (1973) 17-31
7. Collatz L. Numerische Behandlung von Differentialgleichungen (1951), Springer-Verlag, Berlin-Göttingen-Heidelberg
8. Draganescu A., Dupont T.F., and Scott L.R. Failure of the discrete maximum principle for an elliptic finite element method. Math. Comput. 74 (2005) 1-23
9. Forsythe G.E., and Wasow W.R. Finite-Difference Methods for Partial Differential Equations (1960), John Wiley & Sons, New York, London
10. Karátson J., and Korotov S. Discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions. Numer. Math. 99 (2005) 669-698
11. Karátson J., Korotov S., and Křížek M. On discrete maximum principles for nonlinear elliptic problems. Math. Comput. Simulation 76 (2007) 99-108
12. 5 into acute simplices. Discrete Comput. Geom. 36 (2006) 381-390
13. Křížek M., and Qun L. On diagonal dominance of stiffness matrices in 3D. East-West J. Numer. Math. 3 (1995) 59-69
14. Ladyzhenskaya O.A., and Ural'tseva N.N. Linear and Quasilinear Elliptic Equations (1968), Leon Ehrenpreis Academic Press, New York, London
15. Milne W.E. Numerical Solution of Differential Equations (1953), John Wiley & Sons, Chapman & Hall, London, New York
16. Protter M., and Weinberger H. Maximum Principles in Differential Equations (1967), Prentice-Hall, Englewood Cliffs, New Jersey
17. Sperb R. Maximum Principles and their Applications (1981), Academic Press, New York
18. Varga R. Matrix Iterative Analysis (1962), Prentice Hall, New Jersey
19. Varga R. On a discrete maximum principle. SIAM J. Numer. Anal. 3 (1966) 355-359
20. Xu J., and Zikatanov L. A monotone finite element scheme for convection-diffusion equations. Math. Comput. 68 (1999) 1429-1446