Multigrid for the mortar finite element method

SIAM Journal on Numerical Analysis

Volumn 37, Issue 3, 2000, Pages 1029-1052

  Gopalakrishnan, Jayadeep ^a   Pasciak, Joseph E ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Domain decomposition; Finite element method; Mortar; Multigrid; Preconditioning; V cycle

Indexed keywords

EID: 0012550925     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142998341040     Document Type: Article

References (21)

1. Y. ACHDOU AND Y. A. KUZNETSOV, Substructuring preconditioners for finite element methods on nonmatching grids, East-West J. Numer. Math., 3 (1995), pp. 1-28.
2. F. BEN BELGACEM, The mortar finite element method with Lagrange multipliers, Numer. Math., 84 (1999), pp. 2173-2197.
3. C. BERNARDI, Y. MADAY, AND A. T. PATERA, Domain decomposition by the mortar element method, in Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, H. G. Kaper and M. Garbey, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 269-286.
4. C. BERNARDI, Y. MADAY, AND A. T. PATERA, A new nonconforming approach to domain decomposition: The mortar element method, in Nonlinear Partial Differential Equations and Their Applications, H. Brezis and J. L. Lions, eds., Pitman Res. Notes Math. Ser. 299, Longman Scientific and Technical, Harlow, UK, 1994, pp. 13-51.
5. D. BRAESS, W. DAHMEN, AND C. WIENERS, A Multigrid Algorithm for the Mortar Finite Element Method, Technical Report 153, Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Aachen, Germany, 1998.
6. J. H. BRAMBLE, Multigrid Methods, Pitman Res. Notes Math. Ser. 294, Longman Scientific and Technical, Harlow, UK, 1993.
7. J. H. BRAMBLE, J. E. PASCIAK, AND J. XU, The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms, Math. Comp., 56 (1991), pp. 1-34.
8. 2 projection, Math. Comp., 56 (1991), pp. 463-476.
9. J. H. BRAMBLE AND X. ZHANG, The analysis of multigrid methods, in Handbook of Numerical Analysis, Vol. 7, 2000, to appear.
10. S. BRENNER AND L. R. SCOTT, The Mathematical Theory of Finite Element Methods, Texts Appl. Math. 15, Springer-Verlag, New York, 1994.
11. M. A. CASARIN AND O. B. WIDLUND, A hierarchical preconditioner for the mortar finite element method, Electron. Trans. Numer. Anal., 4 (1996), pp. 75-88.
12. J. DESCLOUX, On finite element matrices, SIAM J. Numer. Anal., 2 (1972), pp. 260-265.
13. J. GOPALAKRISHNAN, On the Mortar Finite Element Method, Ph.D. thesis, Texas A&M University, College Station, TX, 1999.
14. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Monographs Stud. Math. 24, Pitman, Boston, London, 1985.
15. R. B. KELLOG, Interpolation Between Subspaces of a Hilbert Space, Technical Note BN-719, University of Maryland, College Park, MD, 1971.
16. J. L. LIONS AND E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications, Vol. I, Springer-Verlag, New York, Heidelberg, 1972.
17. P. OSWALD, Multilevel Finite Element Approximation, Teubner Skripten zur Numerik, B. G. Teubner, Stuttgart, 1994.
18. Y. SAAD, Iterative Methods for Sparse Linear Systems, PWS, Boston, 1996.
19. P. SESHAIYER AND M. SURI, Uniform hp convergence results for the mortar finite element method, Math. Comp., (2000), to appear.
20. J. R. SHEWCHUK, Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator, in First Workshop on Applied Computational Geometry, Association for Computing Machinery, New York, 1996, pp. 124-133.
21. V. THOMÉE, Galerkin Finite Element Methods for Parabolic Problems, Lecture Notes in Math. 1054, Springer-Verlag, Berlin, New York, 1984.