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Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle
Author(s):
Sergey
Korotov;
Michal
Krízek;
Pekka
Neittaanmäki.
Journal:
Math. Comp.
70
(2001),
107-119.
MSC (2000):
Primary 65N30
Posted:
May 23, 2000
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Abstract:
We prove that a discrete maximum principle holds for continuous piecewise linear finite element approximations for the Poisson equation with the Dirichlet boundary condition also under a condition of the existence of some obtuse internal angles between faces of terahedra of triangulations of a given space domain. This result represents a weakened form of the acute type condition for the three-dimensional case.
References:
-
- 1.
- Bertolazzi, E., Discrete conservation and discrete maximum principle for elliptic PDEs, Math. Models Methods Appl. Sci. 8 (1998), 685-711. MR 99h:65185
- 2.
- Bramble, J. H., Hubbard, B. E., New monotone type approximations of elliptic problems, Math. Comp. 18 (1964), 349-367. MR 29:2982
- 3.
- Ciarlet, P. G., Discrete maximum principle for finite difference operators, Aequationes Math. 4 (1970), 338-352. MR 45:1404
- 4.
- Ciarlet, P. G., Raviart, P. A., Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg. 2 (1973), 17-31. MR 51:11992
- 5.
- Feistauer, M., Felcman, J., Rokyta, M., Vlásek, Z., Finite-element solution of flow problems with trailing conditions, J. Comput. Appl. Math. 44 (1992), 131-165. MR 94d:76052
- 6.
- Gilbarg, D., Trudinger, N. S., Elliptic partial differential equations of second order, Springer-Verlag, Berlin-New York, 1977. MR 57:13109
- 7.
- Golias, N. A., Tsiboukis, T. D., An approach to refining three-dimensional tetrahedral meshes based on Delaunay transformations, Internat. J. Numer. Methods Engrg. 37 (1994), 793-812. CMP 94:08
- 8.
- Höhn, W., Mittelmann, H. D., Some remarks on the discrete maximum-principle for finite elements of higher order, Computing 27 (1981), 145-154. MR 83a:65109
- 9.
- Krízek , M., An equilibrium finite element method in three-dimensional elasticity, Apl. Mat. 27 (1982), 46-75. MR 83b:73056
- 10.
- Krízek, M., Qun, L., On diagonal dominance of stiffness matrices in 3D, East-West J. Numer. Math. 3 (1) (1995), 59-69. MR 96f:65153
- 11.
- Krízek, M., Strouboulis, T., How to generate local refinements of unstructured tetrahedral meshes satisfying a regularity ball condition, Numer. Methods Partial Differential Equations, 13 (1997), 201-214. MR 98c:65160
- 12.
- Ong, M. E. G., Uniform refinement of a tetrahedron, SIAM J. Sci. Comput. 15 (1994), 1134-1144. MR 95f:65213
- 13.
- Santos, V. R., On the strong maximum principle for some piecewise linear finite element approximate problems of nonpositive type, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), 473-491.
- 14.
- Stampacchia, G., Le problème de Dirichlet pour les équations elliptiques du second ordre á coefficients discontinus, Ann. Inst. Fourier (Grenoble) 15 (1968), 189-258. MR 33:404
- 15.
- Stoyan, G., On a maximum principle for matrices, and on conservation of monotonicity. With applications to discretization methods., Z. Angew. Math. Mech. 62 (1982), 375-381. MR 83k:65067
- 16.
- Stoyan, G., On maximum principles for monotone matrices, Linear Algebra Appl. 78 (1986), 147-161. MR 87k:65032
- 17.
- Strang, G., Fix, G. J., An analysis of the finite element method, Prentice Hall, Englewood Cliffs, N. J., 1973. MR 56:1747
- 18.
- Varga, R., Matrix iterative analysis, Prentice Hall, New Jersey, 1962. MR 28:1725
- 19.
- Zhang, S., Successive subdivisions of tetrahedra and multigrid methods on tetrahedral meshes, Houston J. Math. 21 (1995), 541-556. MR 96f:65183
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Additional Information:
Sergey
Korotov
Affiliation:
University of Jyväskylä, Department of Mathematical Information Technology, P.O. Box 35, FIN--40351 Jyväskylä, Finland
Email:
korotov@mit.jyu.fi
Michal
Krízek
Affiliation:
Mathematical Institute, Academy of Sciences, Zitná 25, CZ--11567 Prague 1, Czech Republic
Email:
krizek@math.cas.cz
Pekka
Neittaanmäki
Affiliation:
University of Jyväskylä, Department of Mathematical Information Technology, P.O. Box 35, FIN--40351 Jyväskylä, Finland
Email:
pn@mit.jyu.fi
DOI:
10.1090/S0025-5718-00-01270-9
PII:
S 0025-5718(00)01270-9
Keywords:
Maximum principle,
Poisson equation,
weakened acute type condition,
linear tetrahedral finite element
Received by editor(s):
January 26, 1999
Posted:
May 23, 2000
Additional Notes:
The first author was partly supported by the Academy of Finland, Grant no. 752205, and partly by the Mittag-Leffler Institute, Djursholm, Sweden
The second author was supported by the Grant no. 201/98/0528 of the Grant Agency of Czech Republic
Copyright of article:
Copyright
2000,
American Mathematical Society
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