Two simple derivations of universal bounds for the C.B.S. inequality constant

Applications of Mathematics

Volumn 49, Issue 1, 2004, Pages 57-72

  Axelsson, Owe ^a   Blaheta, Radim ^b  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

^b INSTITUTE OF GEONICS   (Czech Republic)

Author keywords

finite element method; h and p refinement; strengthened Cauchy Bunyakowski Schwarz inequality

Indexed keywords

EID: 84867926601     PISSN: 08627940     EISSN: 15729109     Source Type: Journal    
DOI: 10.1023/B:APOM.0000024520.06175.8b     Document Type: Article

References (13)

1. B. Achchab O. Axelsson L. Laayouni A. Souissi 2001 Strengthened Cauchy-Bunyakowski-Schwarz inequality for a three dimensional elasticity system Numer. Linear Algebra Appl. 8 191 205
2. B. Achchab J. Maitre 1996 Estimate of the constant in two strengthened C.B.S. inequalities for F.E.M. systems of 2D elasticity. Applications to multilevel methods and a posteriori error estimators Numer. Linear Algebra Appl. 3 147 159
3. O. Axelsson: On multigrid methods of the two-level type. In: Multigrid Methods, Lecture Notes in Math. 960 (W. Hackbusch, U. Trottenberg, eds.). Springer-Verlag, Berlin, 1982, pp. 352-367.
4. O. Axelsson 1999 Stabilization of algebraic multilevel iteration methods; additive methods Numer. Algorithms 21 23 47
5. O. Axelsson, V. A. Barker: Finite Element Solution of Boundary Value Problems. Theory and Computation. Academic Press, Orlando, 1984, reprinted as SIAM Classics in Applied Mathematics 35, SIAM, Philadelphia, 2001.
6. O. Axelsson I. Gustafsson 1983 Preconditioning and two-level multigrid methods of arbitrary degree of approximation [Report 8120 (July 1981), Department of Mathematics, University of Nijmegen, The Netherlands] Math. Comp. 40 219 242
7. O. Axelsson A. Padiy 1999 On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems SIAM J. Sci. Comput. 20 1807 1830
8. R. Blaheta 1999 Adaptive composite grid methods for problems of plasticity Math. Comput. Simulation 50 123 134
9. R. Blaheta 2003 Nested tetrahedral grids and strengthened C.B.S. inequality Numer. Linear Algebra Appl. 10 619 637
10. M. Jung J. F. Maitre 1999 Some remarks on the constant in the strengthened C.B.S. inequality: estimate for hierarchic finite element discretization of elasticity problems Numer. Methods Partial Differential Equations 15 469 488
11. J. F. Maitre, F. Musy: The contraction number of a class of two-level methods, an exact evaluation for some finite element subspaces and model problems. In: Multigrid Methods, Lecture Notes in Math. 960 (W. Hackbusch, U. Trottenberg, eds.). Springer-Verlag, Berlin, 1982, pp. 535-544.
12. J. NeČas, I. HlaváČek: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam, 1981.
13. S. D. Margenov 1994 Upper bound on the constant in the strengthened C.B.S. inequality for FEM 2D elasticity equations Numer. Linear Algebra Appl. 1 65 74