메뉴 건너뛰기




Volumn 24, Issue 3, 2004, Pages 521-546

Residual a posteriori error estimates for a 3D mortar finite-element method: The Stokes system

Author keywords

A posteriori estimates; Mixed finite elements; Mortar finite element method; Non matching grids; Stabilization techniques; Stokes equations

Indexed keywords

DOMAIN DECOMPOSITION METHODS; ERRORS; MORTAR; NAVIER STOKES EQUATIONS;

EID: 4043094112     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/24.3.521     Document Type: Article
Times cited : (2)

References (26)
  • 2
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • BABuŠKA, I. & RHEINBOLDT, W. C. (1978) Error estimates for adaptive finite element computations. SIAM J. Numer. Anal., 15, 736-754.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babuška, I.1    Rheinboldt, W.C.2
  • 3
    • 0023306715 scopus 로고
    • A feedback finite element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the aposteriori estimator
    • BABUŠKA, I. & MILLER, A. (1987) A feedback finite element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the aposteriori estimator. Comput. Methods Appl. Mech. Engng, 61.
    • (1987) Comput. Methods Appl. Mech. Engng , pp. 61
    • Babuška, I.1    Miller, A.2
  • 4
    • 0026173586 scopus 로고
    • A posteriori error estimates for the Stokes problem
    • BANK, R. E. & WELFERT, B. D. (1991) A posteriori error estimates for the Stokes problem. SIAM J. Numer. Anal., 28, 591-623.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 591-623
    • Bank, R.E.1    Welfert, B.D.2
  • 5
    • 0000451632 scopus 로고    scopus 로고
    • A posteriori error estimation for adaptive discontinuous Galerkin approximations of hyperbolic systems. Discontinuous Galerkin methods (Newport, RI, 1999)
    • Berlin: Springer
    • BARTH, T. & LARSON, M. (2000) A posteriori error estimation for adaptive discontinuous Galerkin approximations of hyperbolic systems. Discontinuous Galerkin methods (Newport, RI, 1999), 363-368. Lecture Notes in Computer Science Engineering, Vol. 11. Berlin: Springer.
    • (2000) Lecture Notes in Computer Science Engineering , vol.11 , pp. 363-368
    • Barth, T.1    Larson, M.2
  • 6
    • 0346947005 scopus 로고    scopus 로고
    • A posteriori error estimates for the 3D stabilized mortar finite element method applied to the Laplace equation
    • to appear
    • BELHACHMI, Z. (2003) A posteriori error estimates for the 3D stabilized mortar finite element method applied to the Laplace equation. M2AN, to appear.
    • (2003) M2AN
    • Belhachmi, Z.1
  • 7
    • 0001476937 scopus 로고    scopus 로고
    • The mixed mortar finite element method for the incompressible Stokes problem: Convergence analysis
    • BEN BELGACEM, F. (2000) The mixed mortar finite element method for the incompressible Stokes problem: convergence analysis. SIAM J. Numer. Anal., 37, 1085-1100.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 1085-1100
    • Ben Belgacem, F.1
  • 8
    • 4043133815 scopus 로고    scopus 로고
    • A stabilized domain decomosition method with non-matching grids for the Stokes problem in three dimensions
    • to appear
    • BEN BELGACEM, F. (2003) A stabilized domain decomosition method with non-matching grids for the Stokes problem in three dimensions. SIAM J. Numer. Anal., to appear.
    • (2003) SIAM J. Numer. Anal.
    • Ben Belgacem, F.1
  • 9
    • 0040141954 scopus 로고    scopus 로고
    • Inf-sup condition for the mortar spectral element discretization of the Stokes problem
    • BEN BELGACEM, F., BERNARDI, C., CHORFI, N. & MADAY, Y. (2000) Inf-sup condition for the mortar spectral element discretization of the Stokes problem. Numer. Math., 85, 257-281.
    • (2000) Numer. Math. , vol.85 , pp. 257-281
    • Ben Belgacem, F.1    Bernardi, C.2    Chorfi, N.3    Maday, Y.4
  • 10
    • 0036792339 scopus 로고    scopus 로고
    • Error indicators for the mortar finite element discretization of the Laplace equation
    • BERNARDI, C. & HECHT, F. (2002) Error indicators for the mortar finite element discretization of the Laplace equation. Math. Comput., 71, 1339-1370.
    • (2002) Math. Comput. , vol.71 , pp. 1339-1370
    • Bernardi, C.1    Hecht, F.2
  • 11
    • 0001625423 scopus 로고    scopus 로고
    • A local regularization operator for triangular and quadrilateral finite elements
    • BERNARDI, C. & GIRAULT, V. (1998) A local regularization operator for triangular and quadrilateral finite elements. SIAM. J. Numer. Anal., 35, 1893-1916.
    • (1998) SIAM. J. Numer. Anal. , vol.35 , pp. 1893-1916
    • Bernardi, C.1    Girault, V.2
  • 12
    • 0002336587 scopus 로고
    • A new non conforming approach to domain decomposition: The mortar element method
    • (Paris, 1989-1991), Pitman Res. Notes Math. Ser., 299. Harlow: Longman Sci. Tech.
    • BERNARDI, C., MADAY, Y. & PATERA, A. T. (1990) A new non conforming approach to domain decomposition: the mortar element method. College de France Seminar, Vol. XI (Paris, 1989-1991), Pitman Res. Notes Math. Ser., 299. Harlow: Longman Sci. Tech., pp. 13-51.
    • (1990) College De France Seminar , vol.11 , pp. 13-51
    • Bernardi, C.1    Maday, Y.2    Patera, A.T.3
  • 13
    • 0009470169 scopus 로고    scopus 로고
    • Stabilization techniques for domain decomposition with non-matching grids
    • (P. Bjostrad, M. Espedal & D. Keyes, eds). Bergen: Domain Decomposition Press
    • BREZZI, F., FRANCA, L. P., MARINI, D. & Russo, A. (1998) Stabilization techniques for domain decomposition with non-matching grids. Domain Decomposition Methods in Sciences and Engineering. (P. Bjostrad, M. Espedal & D. Keyes, eds). Bergen: Domain Decomposition Press, pp. 1-11.
    • (1998) Domain Decomposition Methods in Sciences and Engineering , pp. 1-11
    • Brezzi, F.1    Franca, L.P.2    Marini, D.3    Russo, A.4
  • 14
    • 0001663212 scopus 로고
    • Su un problema al contorno relative al sistema di equazioni di Stokes
    • CATTABRIGA, L. (1961) Su un problema al contorno relative al sistema di equazioni di Stokes. Rend. Sem. Mat. Univ. Padova, 31, 308-340.
    • (1961) Rend. Sem. Mat. Univ. Padova , vol.31 , pp. 308-340
    • Cattabriga, L.1
  • 15
    • 8544220284 scopus 로고
    • Basic Error Estimates for Elliptic Problems
    • (P. G. Ciarlet & J.-L. Lions, eds). Amsterdam
    • CIARLET, P. G. (1991) Basic Error Estimates for Elliptic Problems. Handbook of Numerical Analysis, Vol. II. (P. G. Ciarlet & J.-L. Lions, eds). Amsterdam: pp. 17-351.
    • (1991) Handbook of Numerical Analysis , vol.2 , pp. 17-351
    • Ciarlet, P.G.1
  • 16
    • 84966225938 scopus 로고
    • An adaptive finite element method for linear elliptic problems
    • ERIKSSON, K. & JOHNSON, C. (1988) An adaptive finite element method for linear elliptic problems. Math. Comput., 50, 361-383.
    • (1988) Math. Comput. , vol.50 , pp. 361-383
    • Eriksson, K.1    Johnson, C.2
  • 18
    • 0034352046 scopus 로고    scopus 로고
    • A posteriori error analysis for stabilised finite element approximations of transport problems
    • HOUSTON, P., RANNACHER, R. & SÜLI, E. (2000) A posteriori error analysis for stabilised finite element approximations of transport problems. Comput. Methods Appl. Mech. Engng, 190, 1483-1508.
    • (2000) Comput. Methods Appl. Mech. Engng , vol.190 , pp. 1483-1508
    • Houston, P.1    Rannacher, R.2    Süli, E.3
  • 19
    • 0001481146 scopus 로고
    • Existence, uniqueness and approximation for generalized saddle point problems
    • NICOLAIDES, R. A. (1982) Existence, uniqueness and approximation for generalized saddle point problems. SIAM J. Numer. Anal., 19, 349-357.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 349-357
    • Nicolaides, R.A.1
  • 20
    • 84966200902 scopus 로고
    • Finite element interpolation of nonsmooth functions satisfying boundary conditions
    • SCOTT, L. R. & ZHANG, S. (1990) Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput., 54, 483-493.
    • (1990) Math. Comput. , vol.54 , pp. 483-493
    • Scott, L.R.1    Zhang, S.2
  • 21
    • 0002885640 scopus 로고    scopus 로고
    • A posteriori error analysis and adaptivity for finite element approximations of hyperbolic problems. An introduction to recent developments in theory and numerics for conservation laws (Freiburg/Littenweiler, 1997)
    • Berlin: Springer
    • SÜLI, E. (1999) A posteriori error analysis and adaptivity for finite element approximations of hyperbolic problems. An introduction to recent developments in theory and numerics for conservation laws (Freiburg/ Littenweiler, 1997). Lecture Notes in Computer Science Engineering, Vol. 5. Berlin: Springer, pp. 123-194.
    • (1999) Lecture Notes in Computer Science Engineering , vol.5 , pp. 123-194
    • Süli, E.1
  • 22
    • 34249971216 scopus 로고
    • A posteriori error estimators for the Stokes equations
    • VERFÜRTH, R. (1989) A posteriori error estimators for the Stokes equations. Numer. Math., 55, 309-325.
    • (1989) Numer. Math. , vol.55 , pp. 309-325
    • Verfürth, R.1
  • 24
    • 0033450371 scopus 로고    scopus 로고
    • Error estimates for some quasi-interpolation operators
    • VERFÜRTH, R. (1999) Error estimates for some quasi-interpolation operators. Modél. Math. et Anal. Numer., 33, 695-713.
    • (1999) Modél. Math. Et Anal. Numer. , vol.33 , pp. 695-713
    • Verfürth, R.1
  • 25
    • 4043129610 scopus 로고
    • An extention theorem for finite element spaces with three applications in Numerical Techniques in Continuum Mechanics
    • (W Hackbush & K. Witsch, eds). Kiel
    • WIDLUND, O. B. (1986) An extention theorem for finite element spaces with three applications in Numerical Techniques in Continuum Mechanics. Proc. 2nd GAMM Seminar. (W Hackbush & K. Witsch, eds). Kiel.
    • (1986) Proc. 2nd GAMM Seminar
    • Widlund, O.B.1
  • 26
    • 22844453536 scopus 로고    scopus 로고
    • A residual based error estimator for mortar finite element discretization
    • WOHLMUTH, B. (1999) A residual based error estimator for mortar finite element discretization. Numer. Math., 84, 143-171.
    • (1999) Numer. Math. , vol.84 , pp. 143-171
    • Wohlmuth, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.