메뉴 건너뛰기




Volumn 24, Issue 6, 2003, Pages 2163-2184

Duality estimates and multigrid analysis for saddle point problems arising from mortar discretizations

Author keywords

Dual estimates; Mortar finite elements; Multigrid methods; Nonconforming finite elements; Saddle point problems

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; GEOMETRY; LAGRANGE MULTIPLIERS; PROBLEM SOLVING; THEOREM PROVING;

EID: 0346946937     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502402715     Document Type: Article
Times cited : (14)

References (26)
  • 1
    • 0001804939 scopus 로고
    • Mixed and nonconforming finite element methods: Implementation, post-processing and error estimates
    • D.N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: Implementation, post-processing and error estimates, RAIRO Modél Math. Anal. Numér., 19 (1985), pp. 7-35.
    • (1985) RAIRO Modél Math. Anal. Numér. , vol.19 , pp. 7-35
    • Arnold, D.N.1    Brezzi, F.2
  • 3
    • 0032268117 scopus 로고    scopus 로고
    • Stability estimates of the mortar finite element method for 3-dimensional problems
    • D. Braess and W. Dahmen, Stability estimates of the mortar finite element method for 3-dimensional problems, East-West J. Numer. Math., 6 (1998), pp. 249-263.
    • (1998) East-West J. Numer. Math. , vol.6 , pp. 249-263
    • Braess, D.1    Dahmen, W.2
  • 4
    • 0036954879 scopus 로고    scopus 로고
    • A cascadic multigrid method for mortar elements
    • D. Braess, P. Deuflhard, and K. Lipnikov, A cascadic multigrid method for mortar elements, Computing, 69 (2002), pp. 205-225.
    • (2002) Computing , vol.69 , pp. 205-225
    • Braess, D.1    Deuflhard, P.2    Lipnikov, K.3
  • 5
    • 0000713962 scopus 로고    scopus 로고
    • A multigrid algorithm for the mortar finite element method
    • D. Braess, W. Dahmen, and C. Wieners, A multigrid algorithm for the mortar finite element method, SIAM J. Numer. Anal., 37 (1999), pp. 48-69.
    • (1999) SIAM J. Numer. Anal. , vol.37 , pp. 48-69
    • Braess, D.1    Dahmen, W.2    Wieners, C.3
  • 6
    • 0041800397 scopus 로고    scopus 로고
    • The mortar finite element method with Lagrange multipliers
    • F. Ben Belgacem, The mortar finite element method with Lagrange multipliers, Numer. Math., 84 (1999), pp. 173-197.
    • (1999) Numer. Math. , vol.84 , pp. 173-197
    • Ben Belgacem, F.1
  • 7
    • 0003881705 scopus 로고
    • Mixed and hybrid finite element methods
    • Springer-Verlag, New York
    • F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
    • (1991)
    • Brezzi, F.1    Fortin, M.2
  • 9
    • 0002336587 scopus 로고
    • A new nonconforming approach to domain decomposition: The mortar element method
    • H. Brezzi et al., eds., Paris, France
    • 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. Brezzi et al., eds., Paris, France, 1994, pp. 13-51.
    • (1994) Nonlinear Partial Differential Equations and Their Applications , pp. 13-51
    • Bernardi, C.1    Maday, Y.2    Patera, A.T.3
  • 10
    • 84966255975 scopus 로고
    • Convergence estimates for multigrid algorithms without regularity assumptions
    • J.H. Bramble, J.E. Pasciak, J. Wang, and J. Xu, Convergence estimates for multigrid algorithms without regularity assumptions, Math. Comp., 57 (1991), pp. 23-45.
    • (1991) Math. Comp. , vol.57 , pp. 23-45
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.3    Xu, J.4
  • 11
    • 0030526819 scopus 로고    scopus 로고
    • Multigrid methods for parameter dependent problems
    • S.C. Brenner, Multigrid methods for parameter dependent problems, Math. Model. Numer. Anal., 30 (1996), pp. 265-297.
    • (1996) Math. Model. Numer. Anal. , vol.30 , pp. 265-297
    • Brenner, S.C.1
  • 12
    • 0031070105 scopus 로고    scopus 로고
    • An efficient smoother for the Stokes problem
    • D. Braess and R. Sarazin, An efficient smoother for the Stokes problem, Appl. Numer. Math., 23 (1997), pp. 3-19.
    • (1997) Appl. Numer. Math. , vol.23 , pp. 3-19
    • Braess, D.1    Sarazin, R.2
  • 13
    • 0001677218 scopus 로고
    • Black box multi-grid
    • J.E. Dendy, Black box multi-grid, J. Comput. Phys., 48 (1982), pp. 366-386.
    • (1982) J. Comput. Phys. , vol.48 , pp. 366-386
    • Dendy, J.E.1
  • 14
    • 0012550925 scopus 로고    scopus 로고
    • Multigrid for the mortar finite element method
    • J. Gopalakrishnan and J.E. Pasciak, Multigrid for the mortar finite element method, SIAM J. Numer. Anal., 37 (2000), pp. 1029-1052.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 1029-1052
    • Gopalakrishnan, J.1    Pasciak, J.E.2
  • 16
    • 0029947420 scopus 로고    scopus 로고
    • Non steady-state descriptions of drug permeation through stratum corneum. I: The biphasic, brick-and-mortar model
    • M. Heisig, R. Lieckfeldt, G. Wittum, G. Mazurkevich, and G. Lee, Non steady-state descriptions of drug permeation through stratum corneum. I: The biphasic, brick-and-mortar model, Pharm. Res., 13 (1996), pp. 421-426.
    • (1996) Pharm. Res. , vol.13 , pp. 421-426
    • Heisig, M.1    Lieckfeldt, R.2    Wittum, G.3    Mazurkevich, G.4    Lee, G.5
  • 17
    • 0035322507 scopus 로고    scopus 로고
    • Multiplier spaces for the mortar finite element method in three dimensions
    • C. Kim, R.D. Lazarov, J.E. Pasciak, and P.S. Vassilevski, Multiplier spaces for the mortar finite element method in three dimensions, SIAM J. Numer. Anal., 39, (2001), pp. 519-538.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 519-538
    • Kim, C.1    Lazarov, R.D.2    Pasciak, J.E.3    Vassilevski, P.S.4
  • 19
    • 22844455425 scopus 로고    scopus 로고
    • Multigrid methods for a parameter dependent problem in primal variables
    • J. Schöberl, Multigrid methods for a parameter dependent problem in primal variables, Numer. Math., 84 (1999), pp. 97-119.
    • (1999) Numer. Math. , vol.84 , pp. 97-119
    • Schöberl, J.1
  • 20
    • 84966200902 scopus 로고
    • Finite element interpolation of nonsmooth functions satisfying boundary conditions
    • L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp., 54 (1990), pp. 483-493.
    • (1990) Math. Comp. , vol.54 , pp. 483-493
    • Scott, L.R.1    Zhang, S.2
  • 21
    • 0042730401 scopus 로고    scopus 로고
    • Robust multigrid methods for nearly incompressible elasticity
    • C. Wieners, Robust multigrid methods for nearly incompressible elasticity, Computing, 64 (2000), pp. 289-306.
    • (2000) Computing , vol.64 , pp. 289-306
    • Wieners, C.1
  • 22
    • 0036880243 scopus 로고    scopus 로고
    • A comparison of dual Lagrange multiplier spaces for mortar finite element discretizations
    • B.I. Wohlmuth, A comparison of dual Lagrange multiplier spaces for mortar finite element discretizations, Math. Model. Numer. Anal., 36 (2002), pp. 995-1012.
    • (2002) Math. Model. Numer. Anal. , vol.36 , pp. 995-1012
    • Wohlmuth, B.I.1
  • 23
    • 0012536402 scopus 로고    scopus 로고
    • Discretization methods and iterative solvers based on domain decomposition
    • Springer-Verlag, Heidelberg
    • B.I. Wohlmuth, Discretization methods and iterative solvers based on domain decomposition, Lect. Notes Comput. Sci. Eng. 17, Springer-Verlag, Heidelberg, 2001.
    • (2001) Lect. Notes Comput. Sci. Eng. , vol.17
    • Wohlmuth, B.I.1
  • 24
    • 0008493097 scopus 로고    scopus 로고
    • The coupling of mixed and conforming finite element discretizations
    • J. Mandel, C. Farhat, and X. Cai, eds., Contemp. Math. 218, AMS, Providence, RI
    • C. Wieners and B.I. Wohlmuth, The coupling of mixed and conforming finite element discretizations, in Proceedings of the 10th International Conference on Domain Decomposition, J. Mandel, C. Farhat, and X. Cai, eds., Contemp. Math. 218, AMS, Providence, RI, 1998, pp. 547-554.
    • (1998) Proceedings of the 10th International Conference on Domain Decomposition , pp. 547-554
    • Wieners, C.1    Wohlmuth, B.I.2
  • 25
    • 0010000802 scopus 로고    scopus 로고
    • A general framework for multigrid methods for mortar finite elements
    • Technical report 415, Universität Augsburg, Augsburg, Germany
    • C. Wieners and B.I. Wohlmuth, A General Framework for Multigrid Methods for Mortar Finite Elements, Technical report 415, Universität Augsburg, Augsburg, Germany, 1999.
    • (1999)
    • Wieners, C.1    Wohlmuth, B.I.2
  • 26
    • 0001328840 scopus 로고    scopus 로고
    • A class of smoothers for saddle point problems
    • W. Zulehner, A class of smoothers for saddle point problems, Computing, 65 (2000), pp. 227-246.
    • (2000) Computing , vol.65 , pp. 227-246
    • Zulehner, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.