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Volumn 69, Issue 229, 2000, Pages 121-140

On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form

Author keywords

Mixed finite element methods; Spurious eigenvalues

Indexed keywords


EID: 0034383380     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01072-8     Document Type: Article
Times cited : (139)

References (33)
  • 1
    • 54249116319 scopus 로고    scopus 로고
    • Eigenvalue problems
    • P.G. Ciarlet and J.L. Lions, eds., Elsevier Science Publishers B.V., North Holland
    • I. Babuška and John E. Osborn, Eigenvalue problems, Handbook of Numerical Analysis (P.G. Ciarlet and J.L. Lions, eds.), vol. II, Elsevier Science Publishers B.V., North Holland, 1991, pp. 641-788. MR 92f:65001
    • (1991) Handbook of Numerical Analysis , vol.2 , pp. 641-788
    • Babuška, I.1    Osborn, J.E.2
  • 2
    • 54249116319 scopus 로고    scopus 로고
    • I. Babuška and John E. Osborn, Eigenvalue problems, Handbook of Numerical Analysis (P.G. Ciarlet and J.L. Lions, eds.), vol. II, Elsevier Science Publishers B.V., North Holland, 1991, pp. 641-788. MR 92f:65001
    • MR , vol.92 F , pp. 65001
  • 3
    • 0029342666 scopus 로고    scopus 로고
    • A mixed displacement-based finite element formulation for acoustic fluid-structure interaction
    • K.-J. Bathe, C. Nitikitpaiboon, and X. Wang, A mixed displacement-based finite element formulation for acoustic fluid-structure interaction, Computers & Structures 56 (1995), 225-237. MR 96b:73094
    • (1995) Computers & Structures , vol.56 , pp. 225-237
    • Bathe, K.-J.1    Nitikitpaiboon, C.2    Wang, X.3
  • 4
    • 0029342666 scopus 로고    scopus 로고
    • K.-J. Bathe, C. Nitikitpaiboon, and X. Wang, A mixed displacement-based finite element formulation for acoustic fluid-structure interaction, Computers & Structures 56 (1995), 225-237. MR 96b:73094
    • MR , vol.96 B , pp. 73094
  • 5
    • 0002593092 scopus 로고    scopus 로고
    • Mathematical analysis of a finite element method without spurious solutions for computation od dieletric waveguides
    • A. Bermúdez and D.G. Pedreira, Mathematical analysis of a finite element method without spurious solutions for computation od dieletric waveguides, Numer. Math. 61 (1992), 39-57. MR 92m:65139
    • (1992) Numer. Math. , vol.61 , pp. 39-57
    • Bermúdez, A.1    Pedreira, D.G.2
  • 6
    • 0002593092 scopus 로고    scopus 로고
    • A. Bermúdez and D.G. Pedreira, Mathematical analysis of a finite element method without spurious solutions for computation od dieletric waveguides, Numer. Math. 61 (1992), 39-57. MR 92m:65139
    • MR , vol.92 M , pp. 65139
  • 7
    • 0041055020 scopus 로고    scopus 로고
    • A remark on spurious eigenvalues in a square
    • to appear
    • D. Boffi, R. Duran, and L. Gastaldi, A remark on spurious eigenvalues in a square, Appl. Math. Lett. (1998), to appear.
    • (1998) Appl. Math. Lett.
    • Boffi, D.1    Duran, R.2    Gastaldi, L.3
  • 8
    • 0039276273 scopus 로고    scopus 로고
    • Edge approximation of eigenvalue problems arising from electromagnetics
    • (Désidéri, Le Tallec, Oñate, Périaux, and Stein, eds.), John Wiley & Sons
    • D. Boffi, P. Fernandes, L. Gastaldi, and I. Perugia, Edge approximation of eigenvalue problems arising from electromagnetics, Numerical Methods in Engineering '96 (Désidéri, Le Tallec, Oñate, Périaux, and Stein, eds.), John Wiley & Sons, 1996, pp. 551-556.
    • (1996) Numerical Methods in Engineering '96 , pp. 551-556
    • Boffi, D.1    Fernandes, P.2    Gastaldi, L.3    Perugia, I.4
  • 9
    • 0041055011 scopus 로고    scopus 로고
    • Computational models of electromagnetic resonators: Analysis of edge element approximation
    • To appear
    • _, Computational models of electromagnetic resonators: analysis of edge element approximation, SIAM J. Numer. Anal. (1998), To appear.
    • (1998) SIAM J. Numer. Anal.
  • 10
    • 0022075675 scopus 로고    scopus 로고
    • Stable and semistable low order finite elements for viscous flows
    • J.M. Boland and R. Nicolaides, Stable and semistable low order finite elements for viscous flows, SIAM J. Numer. Anal. 22 (1985), 474-492. MR 86m:65139
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 474-492
    • Boland, J.M.1    Nicolaides, R.2
  • 11
    • 0022075675 scopus 로고    scopus 로고
    • J.M. Boland and R. Nicolaides, Stable and semistable low order finite elements for viscous flows, SIAM J. Numer. Anal. 22 (1985), 474-492. MR 86m:65139
    • MR , vol.86 M , pp. 65139
  • 13
    • 0040974687 scopus 로고    scopus 로고
    • F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer-Verlag, New York, 1991. MR 92d:65187
    • MR , vol.92 D , pp. 65187
  • 14
    • 0001103820 scopus 로고
    • Error estimates for mixed methods
    • J. Falk and John E. Osborn, Error estimates for mixed methods, R.A.I.R.O. Anal. Numer. 4 (1980), 249-277. MR 82j:65076
    • (1980) R.A.I.R.O. Anal. Numer. , vol.4 , pp. 249-277
    • Falk, J.1    Osborn, J.E.2
  • 15
    • 0040460990 scopus 로고    scopus 로고
    • J. Falk and John E. Osborn, Error estimates for mixed methods, R.A.I.R.O. Anal. Numer. 4 (1980), 249-277. MR 82j:65076
    • MR , vol.82 J , pp. 65076
  • 16
    • 0017633213 scopus 로고    scopus 로고
    • An analysis of the convergence of mixed finite element methods
    • M. Fortin, An analysis of the convergence of mixed finite element methods, R.A.I.R.O. Anal. Numer. 11 (1977), 341-354. MR 55:4473
    • (1977) R.A.I.R.O. Anal. Numer. , vol.11 , pp. 341-354
    • Fortin, M.1
  • 17
    • 0017633213 scopus 로고    scopus 로고
    • M. Fortin, An analysis of the convergence of mixed finite element methods, R.A.I.R.O. Anal. Numer. 11 (1977), 341-354. MR 55:4473
    • MR , vol.55 , pp. 4473
  • 18
    • 0030510428 scopus 로고    scopus 로고
    • Mixed finite element methods in fluid structure systems
    • L. Gastaldi, Mixed finite element methods in fluid structure systems, Numer. Math. 74 (1996), 153-176. MR 97e:73053
    • (1996) Numer. Math. , vol.74 , pp. 153-176
    • Gastaldi, L.1
  • 19
    • 0030510428 scopus 로고    scopus 로고
    • L. Gastaldi, Mixed finite element methods in fluid structure systems, Numer. Math. 74 (1996), 153-176. MR 97e:73053
    • MR , vol.97 E , pp. 73053
  • 21
    • 0041162360 scopus 로고    scopus 로고
    • V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations, theory and algorithms, Springer-Verlag, Berlin, 1986. MR 88b:65129
    • MR , vol.88 B , pp. 65129
  • 22
    • 84968510953 scopus 로고    scopus 로고
    • Analysis of some mixed finite element methods related to reduced integration
    • C. Johnson and J. Pitkäranta, Analysis of some mixed finite element methods related to reduced integration, Math. Comp. 38 (1982), 375-400. MR 83d:65287
    • (1982) Math. Comp. , vol.38 , pp. 375-400
    • Johnson, C.1    Pitkäranta, J.2
  • 23
    • 84968510953 scopus 로고    scopus 로고
    • C. Johnson and J. Pitkäranta, Analysis of some mixed finite element methods related to reduced integration, Math. Comp. 38 (1982), 375-400. MR 83d:65287
    • MR , vol.83 D , pp. 65287
  • 24
    • 0009934862 scopus 로고    scopus 로고
    • Approximation in variationally posed eigenvalue problems
    • W.G. Kolata, Approximation in variationally posed eigenvalue problems, Numer. Math. 29 (1978), 159-171. MR 80a:49077
    • (1978) Numer. Math. , vol.29 , pp. 159-171
    • Kolata, W.G.1
  • 25
    • 0009934862 scopus 로고    scopus 로고
    • W.G. Kolata, Approximation in variationally posed eigenvalue problems, Numer. Math. 29 (1978), 159-171. MR 80a:49077
    • MR , vol.80 A , pp. 49077
  • 26
    • 84966220668 scopus 로고    scopus 로고
    • Eigenvalue approximation by mixed and hybrid methods
    • B. Mercier, J. Osborn, J. Rappaz, and P.A. Raviart, Eigenvalue approximation by mixed and hybrid methods, Math. Comp. 36 (1981), 427-453. MR 82b:65108
    • (1981) Math. Comp. , vol.36 , pp. 427-453
    • Mercier, B.1    Osborn, J.2    Rappaz, J.3    Raviart, P.A.4
  • 27
    • 84966220668 scopus 로고    scopus 로고
    • B. Mercier, J. Osborn, J. Rappaz, and P.A. Raviart, Eigenvalue approximation by mixed and hybrid methods, Math. Comp. 36 (1981), 427-453. MR 82b:65108
    • MR , vol.82 B , pp. 65108
  • 28
    • 0039868098 scopus 로고
    • Eigenvalue approximations by mixed methods
    • (R. Vichnevetsky and R. Stepleman, eds.), New Brunswick
    • John E. Osborn, Eigenvalue approximations by mixed methods, Advances in Computer Methods for Partial Differential Equations III (R. Vichnevetsky and R. Stepleman, eds.), New Brunswick, 1979, pp. 158-161. MR 82b:65024
    • (1979) Advances in Computer Methods for Partial Differential Equations III , pp. 158-161
    • Osborn, J.E.1
  • 29
    • 0039276275 scopus 로고    scopus 로고
    • John E. Osborn, Eigenvalue approximations by mixed methods, Advances in Computer Methods for Partial Differential Equations III (R. Vichnevetsky and R. Stepleman, eds.), New Brunswick, 1979, pp. 158-161. MR 82b:65024
    • MR , vol.82 B , pp. 65024
  • 31
    • 0031519975 scopus 로고    scopus 로고
    • On mixed elements for acoustic fluid-structure interactions
    • X. Wang and K.-J. Bathe, On mixed elements for acoustic fluid-structure interactions, Math. Models Methods Appl. Sci. 7 (1997), no. 3, 329-343. MR 98c:73068
    • (1997) Math. Models Methods Appl. Sci. , vol.7 , Issue.3 , pp. 329-343
    • Wang, X.1    Bathe, K.-J.2
  • 32
    • 0031519975 scopus 로고    scopus 로고
    • X. Wang and K.-J. Bathe, On mixed elements for acoustic fluid-structure interactions, Math. Models Methods Appl. Sci. 7 (1997), no. 3, 329-343. MR 98c:73068
    • MR , vol.98 C , pp. 73068
  • 33
    • 0027557839 scopus 로고
    • Edge elements and what they can do for you
    • J.P. Webb, Edge elements and what they can do for you, IEEE Trans. on Magnetics 29 (1993), 1460-1465.
    • (1993) IEEE Trans. on Magnetics , vol.29 , pp. 1460-1465
    • Webb, J.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.