메뉴 건너뛰기




Volumn 46, Issue 3, 2008, Pages 1190-1211

A locally divergence-free interior penalty method for two-dimensional curl-curl problems

Author keywords

Curl curl problem; Graded meshes; Interior penalty methods; Locally divergence free; Maxwell eigenproblem

Indexed keywords

CURL-CURL PROBLEM; GRADED MESHES; INTERIOR PENALTY METHODS; LOCALLY DIVERGENCE-FREE; MAXWELL EIGENPROBLEM;

EID: 44649139937     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/060671760     Document Type: Article
Times cited : (57)

References (44)
  • 2
    • 0032046927 scopus 로고    scopus 로고
    • The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges
    • TH. APEL AND S. NICAISE, The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges, Math. Methods Appl. Sci., 21 (1998), pp. 519-549.
    • (1998) Math. Methods Appl. Sci , vol.21 , pp. 519-549
    • APEL, T.1    NICAISE, S.2
  • 3
    • 0035630247 scopus 로고    scopus 로고
    • Crouzeix-Raviart type finite elements on anisotropic meshes
    • TH. APEL, S. NICAISE, AND J. SCHÖBERL, Crouzeix-Raviart type finite elements on anisotropic meshes, Numer. Math., 89 (2001), pp. 193-223.
    • (2001) Numer. Math , vol.89 , pp. 193-223
    • APEL, T.1    NICAISE, S.2    SCHÖBERL, J.3
  • 4
    • 0029755025 scopus 로고    scopus 로고
    • Graded mesh refinement and error estimates for finite element solutions of elliptic boundary value problems in non-smooth domains
    • TH. APEL, A.-M. SANDIG, AND J. R. WHITEMAN, Graded mesh refinement and error estimates for finite element solutions of elliptic boundary value problems in non-smooth domains, Math. Methods Appl. Sci., 19 (1996), pp. 63-85.
    • (1996) Math. Methods Appl. Sci , vol.19 , pp. 63-85
    • APEL, T.1    SANDIG, A.-M.2    WHITEMAN, J.R.3
  • 5
    • 44649091366 scopus 로고    scopus 로고
    • The singular complement method
    • N. Debit, M. Garbey, R. Hoppe, D. Keyes, Y. Kuznetsov, and J. Périaux, eds, CIMNE, Barcelona
    • F. ASSOUS, P. CIARLET, JR., S. LABRUNIE, AND S. LOHRENGEL, The singular complement method, in Domain Decomposition Methods in Science and Engineering, N. Debit, M. Garbey, R. Hoppe, D. Keyes, Y. Kuznetsov, and J. Périaux, eds., CIMNE, Barcelona, 2002, pp. 161-189.
    • (2002) Domain Decomposition Methods in Science and Engineering , pp. 161-189
    • ASSOUS, F.1    CIARLET JR., P.2    LABRUNIE, S.3    LOHRENGEL, S.4
  • 6
    • 0032378152 scopus 로고    scopus 로고
    • F. ASSOUS, P. CIARLET, JR., AND E. SONNENDRÜCKER, Resolution of the Maxwell equation in a domain with reentrant corners, M2AN Math. Model. Numer. Anal., 32 (1998), pp. 359-389.
    • F. ASSOUS, P. CIARLET, JR., AND E. SONNENDRÜCKER, Resolution of the Maxwell equation in a domain with reentrant corners, M2AN Math. Model. Numer. Anal., 32 (1998), pp. 359-389.
  • 7
    • 54249116319 scopus 로고
    • Eigenvalue problems
    • P. G. Ciarlet and J. L. Lions, eds, North-Holland, Amsterdam
    • I. BABUŠKA AND J. OSBORN, Eigenvalue problems, in Handbook of Numerical Analysis II, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 1991, pp. 641-787.
    • (1991) Handbook of Numerical Analysis II , pp. 641-787
    • BABUŠKA, I.1    OSBORN, J.2
  • 8
    • 0034556469 scopus 로고    scopus 로고
    • Fortin operators and discrete compactness for edge elements
    • D. BOFFI, Fortin operators and discrete compactness for edge elements, Numer. Math., 87 (2000), pp. 229-246.
    • (2000) Numer. Math , vol.87 , pp. 229-246
    • BOFFI, D.1
  • 9
    • 34447096192 scopus 로고    scopus 로고
    • Approximation of eigenvalues in mixed form, discrete compactness property, and application to hp mixed finite elements
    • D. BOFFI, Approximation of eigenvalues in mixed form, discrete compactness property, and application to hp mixed finite elements, Comput. Methods Appl. Mech. Engrg., 196 (2007), pp. 3672-3681.
    • (2007) Comput. Methods Appl. Mech. Engrg , vol.196 , pp. 3672-3681
    • BOFFI, D.1
  • 11
    • 0000807589 scopus 로고    scopus 로고
    • Computational models of electromagnetic resonators; Analysis of edge element approximation
    • D. BOFFI, P. FERNANDES, L. GASTALDI, AND I. PERUGIA, Computational models of electromagnetic resonators; Analysis of edge element approximation, SIAM J. Numer. Anal., 36 (1999), pp. 1264-1290.
    • (1999) SIAM J. Numer. Anal , vol.36 , pp. 1264-1290
    • BOFFI, D.1    FERNANDES, P.2    GASTALDI, L.3    PERUGIA, I.4
  • 12
    • 32644442914 scopus 로고    scopus 로고
    • Edge element computation of Maxwell's eigenvalues on general quadrilateral meshes
    • D. BOFFI, F. KIKUCHI, AND J. SCHÖBERL, Edge element computation of Maxwell's eigenvalues on general quadrilateral meshes, Math. Models Methods Appl. Sci., 16 (2006), pp. 265-273.
    • (2006) Math. Models Methods Appl. Sci , vol.16 , pp. 265-273
    • BOFFI, D.1    KIKUCHI, F.2    SCHÖBERL, J.3
  • 14
    • 23944447733 scopus 로고    scopus 로고
    • Finite element methods
    • E. Stein, R. de Borst, and T. J. R. Hughes, eds, Wiley, Weinheim, Germany
    • S. C. BRENNER AND C. CARSTENSEN, Finite element methods, in Encyclopedia of Computational Mechanics, E. Stein, R. de Borst, and T. J. R. Hughes, eds., Wiley, Weinheim, Germany, 2004, pp. 73-118.
    • (2004) Encyclopedia of Computational Mechanics , pp. 73-118
    • BRENNER, S.C.1    CARSTENSEN, C.2
  • 15
    • 34447106394 scopus 로고    scopus 로고
    • A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations
    • S. C. BRENNER, F. LI, AND L.-Y. SUNG, A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations, Math. Comp., 76 (2007), pp. 573-595.
    • (2007) Math. Comp , vol.76 , pp. 573-595
    • BRENNER, S.C.1    LI, F.2    SUNG, L.-Y.3
  • 16
    • 55349107737 scopus 로고    scopus 로고
    • A weakly over-penalized nonsymmetric interior penalty method, J. Numerical Analysis, Industrial and Applied Mathematics
    • to appear
    • S. C. BRENNER AND L. OWENS, A weakly over-penalized nonsymmetric interior penalty method, J. Numerical Analysis, Industrial and Applied Mathematics, to appear.
    • BRENNER, S.C.1    OWENS, L.2
  • 19
    • 35548982113 scopus 로고    scopus 로고
    • Discontinuous Galerkin approximation of the Maxwell eigenproblem
    • A. BUFFA AND I. PERUGIA, Discontinuous Galerkin approximation of the Maxwell eigenproblem, SIAM J. Numer. Anal., 44 (2006), pp. 2198-2226.
    • (2006) SIAM J. Numer. Anal , vol.44 , pp. 2198-2226
    • BUFFA, A.1    PERUGIA, I.2
  • 20
    • 0034446186 scopus 로고    scopus 로고
    • On the convergence of Galerkin finite element approximations of electromagnetic eigenproblems
    • S. CAORSI, P. FERNANDES, AND M. RAFFETTO, On the convergence of Galerkin finite element approximations of electromagnetic eigenproblems, SIAM J. Numer. Anal., 38 (2000), pp. 580-607.
    • (2000) SIAM J. Numer. Anal , vol.38 , pp. 580-607
    • CAORSI, S.1    FERNANDES, P.2    RAFFETTO, M.3
  • 21
    • 0035627702 scopus 로고    scopus 로고
    • Spurious-free approximations of electromagnetic eigenproblems by means of Nédélec-type elements
    • S. CAORSI, P. FERNANDES, AND M. RAFFETTO, Spurious-free approximations of electromagnetic eigenproblems by means of Nédélec-type elements, M2AN Math. Model. Numer. Anal., 35 (2001), pp. 331-358.
    • (2001) M2AN Math. Model. Numer. Anal , vol.35 , pp. 331-358
    • CAORSI, S.1    FERNANDES, P.2    RAFFETTO, M.3
  • 23
    • 84988168833 scopus 로고
    • A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
    • M. COSTABEL, A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains, Math. Methods Appl. Sci., 12 (1990), pp. 365-368.
    • (1990) Math. Methods Appl. Sci , vol.12 , pp. 365-368
    • COSTABEL, M.1
  • 24
    • 0000152459 scopus 로고
    • A coercive bilinear form for Maxwell's equations
    • M. COSTABEL, A coercive bilinear form for Maxwell's equations, J. Math. Anal. Appl., 157 (1991), pp. 527-541.
    • (1991) J. Math. Anal. Appl , vol.157 , pp. 527-541
    • COSTABEL, M.1
  • 25
    • 0033078434 scopus 로고    scopus 로고
    • Maxwell and Lamé eigenvalues on polyhedra
    • M. COSTABEL AND M. DAUGE, Maxwell and Lamé eigenvalues on polyhedra, Math. Methods Appl. Sci., 22 (1999), pp. 243-258.
    • (1999) Math. Methods Appl. Sci , vol.22 , pp. 243-258
    • COSTABEL, M.1    DAUGE, M.2
  • 26
    • 0034382191 scopus 로고    scopus 로고
    • Singularities of electromagnetic fields in polyhedral domains
    • M. COSTABEL AND M. DAUGE, Singularities of electromagnetic fields in polyhedral domains, Arch. Ration. Mech. Anal., 151 (2000), pp. 221-276.
    • (2000) Arch. Ration. Mech. Anal , vol.151 , pp. 221-276
    • COSTABEL, M.1    DAUGE, M.2
  • 27
    • 0036912227 scopus 로고    scopus 로고
    • Weighted regularisation of Maxwell equations in polyhedral domains
    • M. COSTABEL AND M. DAUGE, Weighted regularisation of Maxwell equations in polyhedral domains, Numer. Math., 93 (2002), pp. 239-277.
    • (2002) Numer. Math , vol.93 , pp. 239-277
    • COSTABEL, M.1    DAUGE, M.2
  • 29
    • 17144414595 scopus 로고    scopus 로고
    • Exponential convergence of hp-FEM for Maxwell equations with weighted regularization in polygonal domains
    • M. COSTABEL, M. DAUGE, AND G. SCHWAB, Exponential convergence of hp-FEM for Maxwell equations with weighted regularization in polygonal domains, Math. Models Methods Appl. Sci., 15 (2005), pp. 575-622.
    • (2005) Math. Models Methods Appl. Sci , vol.15 , pp. 575-622
    • COSTABEL, M.1    DAUGE, M.2    SCHWAB, G.3
  • 30
    • 0015762231 scopus 로고
    • Conforming and nonconforming finite element methods for solving the stationary Stokes equations 1
    • M. CROUZEIX AND P.-A. RAVIART, Conforming and nonconforming finite element methods for solving the stationary Stokes equations 1, RAIRO Anal. Numér., 7 (1973), pp. 33-75.
    • (1973) RAIRO Anal. Numér , vol.7 , pp. 33-75
    • CROUZEIX, M.1    RAVIART, P.-A.2
  • 32
    • 0038042416 scopus 로고    scopus 로고
    • A singular field method for Maxwell's equations: Numerical aspects for 2D magneto statics
    • C. HAZARD AND S. LOHRENGEL, A singular field method for Maxwell's equations: Numerical aspects for 2D magneto statics, SIAM J. Numer. Anal., 40 (2002), pp. 1021-1040.
    • (2002) SIAM J. Numer. Anal , vol.40 , pp. 1021-1040
    • HAZARD, C.1    LOHRENGEL, S.2
  • 33
    • 85095827382 scopus 로고    scopus 로고
    • Finite elements in computational electromagnetism
    • R. HIPTMAIR, Finite elements in computational electromagnetism, Acta Numer., 11 (2002), pp. 237-339.
    • (2002) Acta Numer , vol.11 , pp. 237-339
    • HIPTMAIR, R.1
  • 34
    • 25444439239 scopus 로고    scopus 로고
    • Interior penalty method for the indefinite time-harmonic Maxwell equation
    • P. HOUSTON, I. PERUGIA, A. SCHNEEBELI, AND D. SCHÖTZAU, Interior penalty method for the indefinite time-harmonic Maxwell equation, Numer. Math., 100 (2005), pp. 485-518.
    • (2005) Numer. Math , vol.100 , pp. 485-518
    • HOUSTON, P.1    PERUGIA, I.2    SCHNEEBELI, A.3    SCHÖTZAU, D.4
  • 35
    • 25444439279 scopus 로고    scopus 로고
    • Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case
    • P. HOUSTON, I. PERUGIA, A. SCHNEEBELI, AND D. SCHÖTZAU, Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case, M2AN Math. Model. Numer. Anal., 39 (2005), pp. 727-753.
    • (2005) M2AN Math. Model. Numer. Anal , vol.39 , pp. 727-753
    • HOUSTON, P.1    PERUGIA, I.2    SCHNEEBELI, A.3    SCHÖTZAU, D.4
  • 36
    • 20144385612 scopus 로고    scopus 로고
    • Mixed discontinuous Galerkin approximation of the Maxwell operator
    • P. HOUSTON, I. PERUGIA, AND D. SCHÖTZAU, Mixed discontinuous Galerkin approximation of the Maxwell operator, SIAM J. Numer. Anal., 42 (2004), pp. 434-459.
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 434-459
    • HOUSTON, P.1    PERUGIA, I.2    SCHÖTZAU, D.3
  • 37
    • 17444426685 scopus 로고    scopus 로고
    • Mixed discontinuous Galerkin approximation of the Maxwell operator: Non-stabilized formulation
    • P. HOUSTON, I. PERUGIA, AND D. SCHÖTZAU, Mixed discontinuous Galerkin approximation of the Maxwell operator: Non-stabilized formulation, J. Sci. Comput., 22/23 (2005), pp. 315-346.
    • (2005) J. Sci. Comput , vol.22-23 , pp. 315-346
    • HOUSTON, P.1    PERUGIA, I.2    SCHÖTZAU, D.3
  • 43
    • 0037073023 scopus 로고    scopus 로고
    • Stabilized interior penalty methods for the time-harmonic Maxwell equations
    • I. PERUGIA, D. SCHÖTZAU, AND P. MONK, Stabilized interior penalty methods for the time-harmonic Maxwell equations, Comput. Methods. Appl. Mech. Engrg., 191 (2002), pp. 4675-4697.
    • (2002) Comput. Methods. Appl. Mech. Engrg , vol.191 , pp. 4675-4697
    • PERUGIA, I.1    SCHÖTZAU, D.2    MONK, P.3
  • 44
    • 84966217446 scopus 로고
    • An observation concerning Ritz-Galerkin methods with indefinite bilinear forms
    • A. SCHATZ, An observation concerning Ritz-Galerkin methods with indefinite bilinear forms, Math. Comp., 28 (1974), pp. 959-962.
    • (1974) Math. Comp , vol.28 , pp. 959-962
    • SCHATZ, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.