A preconditioner based on domain decomposition for h-p finite-element approximation on quasi-uniform meshes

SIAM Journal on Numerical Analysis

Volumn 33, Issue 4, 1996, Pages 1358-1376

  Ainsworth, Mark ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Domain decomposition; h p version finite element method; Preconditioning

Indexed keywords

EID: 0001146007     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142993258221     Document Type: Article

References (11)

1. O. AXELSSON AND V. A. BARKER, Finite Element Approximation of Boundary Value Problems, Academic Press, New York, 1984.
2. I. BABUSKA, A. CRAIG, J. MANDEL, AND J. PITKARANTA, Efficient preconditioning for the p version finite element method in two dimensions, SIAM J. Numer. Anal., 28 (1991), pp. 624-661.
3. I. BABUSKA, I. N. KATZ, AND B. SZABO, The p version of the finite element method, SIAM J. Numer. Anal., 18 (1981), pp. 515-545.
4. I. BABUSKA AND M. SURI, The h-p version of the finite element method with quasi-uniform meshes, RAIRO Modél. Mat. Anal. Numér., 21, 1987, pp. 199-238.
5. _ , The treatment of non-homogeneous Dirichlet boundary conditions by the p-version finite element method, Numer. Math., 55 (1989), pp. 97-121.
6. J. H. BRAMBLE, J. E. PASCIAK, AND A. H. SCHATZ, The construction of preconditioned for elliptic problems by substructuring, Math. Comp., 47 (1986), pp. 103-135.
7. J. H. BRAMBLE, Multigrid methods, Pitman Res. Notes, Amsterdam, 294 (1993).
8. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1980.
9. M. DRYJA AND O. B. WIDLUND, Towards a unified theory of domain decomposition algorithms for elliptic problems, in Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. F. Chan et al., eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990, pp. 3-21.
10. T. J. RIVLIN, The Chebyshev Polynomials, Wiley-Interscience, New York, 1974.
11. O. B. WIDLUND, Iterative substructuring methods: Algorithms and theory for elliptic problems in the plane, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski et al., eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1988, pp. 113-128.