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Volumn 44, Issue 4, 2006, Pages 1721-1734

The L2 norm error estimates for the div least-squares method

Author keywords

Elasticity; Elliptic equations; Error estimate; Incom pressible Newtonian flow; Least squares method; Stokes

Indexed keywords

ELASTICITY; LEAST SQUARES APPROXIMATIONS; LINEAR EQUATIONS; NEWTONIAN FLOW;

EID: 34547939124     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/050636504     Document Type: Article
Times cited : (36)

References (20)
  • 1
    • 0034386185 scopus 로고    scopus 로고
    • D. N. ARNOLD, R. S. FALK, AND R. WINTHER, Multigrid in H(div) and H(curl), Numer. Math., 85 (2000), pp. 197-218.
    • D. N. ARNOLD, R. S. FALK, AND R. WINTHER, Multigrid in H(div) and H(curl), Numer. Math., 85 (2000), pp. 197-218.
  • 2
    • 84966251556 scopus 로고
    • Least-squares methods for elliptic systems
    • A. AZIZ, R. KELLOGG, AND A. STEPHENS, Least-squares methods for elliptic systems, Math. Comp., 44 (1985), pp. 53-70.
    • (1985) Math. Comp , vol.44 , pp. 53-70
    • AZIZ, A.1    KELLOGG, R.2    STEPHENS, A.3
  • 3
    • 33644512080 scopus 로고    scopus 로고
    • On least-squares finite element methods for the Poisson equation and their connection to the Dirichlet and Kelvin principles
    • P. BOCHEV AND M. GUNZBURGER, On least-squares finite element methods for the Poisson equation and their connection to the Dirichlet and Kelvin principles, SIAM J. Numer. Anal., 43 (2005), pp. 340-362.
    • (2005) SIAM J. Numer. Anal , vol.43 , pp. 340-362
    • BOCHEV, P.1    GUNZBURGER, M.2
  • 4
    • 0031518552 scopus 로고    scopus 로고
    • A least-squares approach based on a discrete minus one inner product for first order system
    • J. H. BRAMBLE, R. D. LAZAROV, AND J. E. PASCIAK, A least-squares approach based on a discrete minus one inner product for first order system, Math. Comp., 66 (1997), pp. 935-955.
    • (1997) Math. Comp , vol.66 , pp. 935-955
    • BRAMBLE, J.H.1    LAZAROV, R.D.2    PASCIAK, J.E.3
  • 5
    • 34250118577 scopus 로고    scopus 로고
    • F. BREZZI, J. DOUGLAS, JR., AND L. MARINI, TWO families of mixed finite elements for second order elliptic problems, Numer. Math., 47 (1985), pp. 217-235.
    • F. BREZZI, J. DOUGLAS, JR., AND L. MARINI, TWO families of mixed finite elements for second order elliptic problems, Numer. Math., 47 (1985), pp. 217-235.
  • 6
    • 0028747782 scopus 로고
    • First-order system least squares for second-order partial differential equations: PartI
    • Z. CAI, R. LAZAROV, T. A. MANTEUFFEL, AND S. F. MCCORMICK, First-order system least squares for second-order partial differential equations: PartI, SIAM J. Numer. Anal., 31 (1994), pp. 1785-1799.
    • (1994) SIAM J. Numer. Anal , vol.31 , pp. 1785-1799
    • CAI, Z.1    LAZAROV, R.2    MANTEUFFEL, T.A.3    MCCORMICK, S.F.4
  • 7
    • 18444369375 scopus 로고    scopus 로고
    • Least-squares methods for incompressible Newtonian fluid flow: Linear stationary problems
    • Z. CAI, B. LEE, AND P. WANG, Least-squares methods for incompressible Newtonian fluid flow: Linear stationary problems, SIAM J. Numer. Anal., 42 (2004), pp. 843-859.
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 843-859
    • CAI, Z.1    LEE, B.2    WANG, P.3
  • 8
    • 10144254912 scopus 로고    scopus 로고
    • Least-squares methods for linear elasticity
    • Z. CAI AND G. STARKE, Least-squares methods for linear elasticity, SIAM J. Numer. Anal., 42 (2004), pp. 826-842.
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 826-842
    • CAI, Z.1    STARKE, G.2
  • 9
    • 0024750086 scopus 로고
    • Convergence studies of least-squares finite elements for first order systems
    • G. F. CAREY AND Y. SHEN, Convergence studies of least-squares finite elements for first order systems, Comm. Appl. Numer. Methods, 5 (1989), pp. 427-434.
    • (1989) Comm. Appl. Numer. Methods , vol.5 , pp. 427-434
    • CAREY, G.F.1    SHEN, Y.2
  • 10
    • 0025496931 scopus 로고
    • A least-squares finite element method for the Helmholtz equation
    • C. L. CHANG, A least-squares finite element method for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg., 83 (1990), pp. 1-7.
    • (1990) Comput. Methods Appl. Mech. Engrg , vol.83 , pp. 1-7
    • CHANG, C.L.1
  • 12
    • 0021611242 scopus 로고
    • On the accuracy of least squares methods in the presence of corner singularities
    • C. L. COX AND G. FIX, On the accuracy of least squares methods in the presence of corner singularities, Comput. Math. Appl., 10 (1984), pp. 463-475.
    • (1984) Comput. Math. Appl , vol.10 , pp. 463-475
    • COX, C.L.1    FIX, G.2
  • 13
    • 0018301581 scopus 로고
    • On the finite element methods of least-squares type
    • G. FIX, M. GUNZBURGER, AND R. NICOLAIDES, On the finite element methods of least-squares type, Comput. Math. Appl., 5 (1979), pp. 87-98.
    • (1979) Comput. Math. Appl , vol.5 , pp. 87-98
    • FIX, G.1    GUNZBURGER, M.2    NICOLAIDES, R.3
  • 14
    • 0040455480 scopus 로고
    • A least-square decomposition method for solving elliptic systems
    • D. C. JESPERSEN, A least-square decomposition method for solving elliptic systems, Math. Comp., 31 (1977), pp. 873-880.
    • (1977) Math. Comp , vol.31 , pp. 873-880
    • JESPERSEN, D.C.1
  • 15
    • 0027147423 scopus 로고
    • Optimal least-squares finite element method for elliptic problems
    • B. N. JIANG AND L. A. POVINELLI, Optimal least-squares finite element method for elliptic problems, Comput. Methods Appl. Mech. Engrg., 102 (1993), pp. 199-212.
    • (1993) Comput. Methods Appl. Mech. Engrg , vol.102 , pp. 199-212
    • JIANG, B.N.1    POVINELLI, L.A.2
  • 16
    • 0015564858 scopus 로고
    • Use of the least squares criterion in the finite element formulation
    • P. P. LYNN AND S. K. ARYA, Use of the least squares criterion in the finite element formulation, Internat. J. Numer. Methods Engrg., 6 (1973), pp. 75-88.
    • (1973) Internat. J. Numer. Methods Engrg , vol.6 , pp. 75-88
    • LYNN, P.P.1    ARYA, S.K.2
  • 17
    • 0028517692 scopus 로고
    • Least-squares mixed finite elements for second-order elliptic problems
    • A. I. PEHLIVANOV, G. F. CAREY, AND R. D. LAZAROV, Least-squares mixed finite elements for second-order elliptic problems, SIAM J. Numer. Anal., 31 (1994), pp. 1368-1377.
    • (1994) SIAM J. Numer. Anal , vol.31 , pp. 1368-1377
    • PEHLIVANOV, A.I.1    CAREY, G.F.2    LAZAROV, R.D.3
  • 18
    • 0001492022 scopus 로고
    • Convergence of least squares finite elements for first order ODE systems
    • A. I. PEHLIVANOV, G. F. CAREY, R. D. LAZAROV, AND Y. SHEN, Convergence of least squares finite elements for first order ODE systems, Computing, 51 (1993), pp. 111-123.
    • (1993) Computing , vol.51 , pp. 111-123
    • PEHLIVANOV, A.I.1    CAREY, G.F.2    LAZAROV, R.D.3    SHEN, Y.4
  • 19
    • 0001175293 scopus 로고
    • A mixed finite element method for 2nd order elliptic problems, Mathematical Aspects of Finite Element Methods
    • I. Galligani and E. Magenes, eds, Springer, Berlin
    • P. A. RAVIART AND J. M. THOMAS, A mixed finite element method for 2nd order elliptic problems, Mathematical Aspects of Finite Element Methods, Lecture Notes in Math. 606, I. Galligani and E. Magenes, eds., Springer, Berlin, 1977, pp. 292-315.
    • (1977) Lecture Notes in Math , vol.606 , pp. 292-315
    • RAVIART, P.A.1    THOMAS, J.M.2
  • 20
    • 0034401758 scopus 로고    scopus 로고
    • Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems
    • D. YANG, Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems, Math. Comp., 69 (2000), pp. 929-963.
    • (2000) Math. Comp , vol.69 , pp. 929-963
    • YANG, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.