메뉴 건너뛰기




Volumn 15, Issue 4, 2005, Pages 575-622

Exponential convergence of hp-FEM for maxwell equations with weighted regularization in polygonal domains

Author keywords

Exponential convergence; Hp version; Maxwell equations; Weighted regularisation

Indexed keywords


EID: 17144414595     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202505000480     Document Type: Article
Times cited : (65)

References (35)
  • 1
    • 0035850687 scopus 로고    scopus 로고
    • Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes
    • M. Ainsworth and J. Coyle, Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes, Comput. Meth. Appl. Mech. Engrg. 190 (2001) 6709-6733.
    • (2001) Comput. Meth. Appl. Mech. Engrg. , vol.190 , pp. 6709-6733
    • Ainsworth, M.1    Coyle, J.2
  • 2
    • 0141962816 scopus 로고    scopus 로고
    • Hp-approximation theory for BDFM and RT finite elements on quadrilaterals
    • electronic
    • M. Ainsworth and K. Pinchedez, hp-approximation theory for BDFM and RT finite elements on quadrilaterals, SIAM J. Numer. Anal. 40 (2002) 2047-2068 (electronic) (2003).
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 2047-2068
    • Ainsworth, M.1    Pinchedez, K.2
  • 3
    • 0032046927 scopus 로고    scopus 로고
    • The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges
    • T. Apel and S. Nicaise, The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges, Math. Meth. Appl. Sci. 21 (1998) 519-549.
    • (1998) Math. Meth. Appl. Sci. , vol.21 , pp. 519-549
    • Apel, T.1    Nicaise, S.2
  • 4
    • 0000240803 scopus 로고
    • Error estimates for the combined h and p versions of the finite element method
    • I. Babuška and M. R. Dorr, Error estimates for the combined h and p versions of the finite element method, Numer. Math. 37 (1981) 257-277.
    • (1981) Numer. Math. , vol.37 , pp. 257-277
    • Babuška, I.1    Dorr, M.R.2
  • 5
    • 0001003242 scopus 로고
    • Regularity of the solution of elliptic problems with piece-wise analytic data. I. Boundary value problems for linear elliptic equation of second order
    • I. Babuška and B. Q. Guo, Regularity of the solution of elliptic problems with piece-wise analytic data. I. Boundary value problems for linear elliptic equation of second order, SIAM J. Math. Anal. 19 (1988) 172-203.
    • (1988) SIAM J. Math. Anal. , vol.19 , pp. 172-203
    • Babuška, I.1    Guo, B.Q.2
  • 6
    • 0001624937 scopus 로고
    • Regularity of the solution of elliptic problems with piece-wise analytic data. II. The trace spaces and application to the boundary value problems with nonhomogeneous boundary conditions
    • I. Babuška and B. Q. Guo, Regularity of the solution of elliptic problems with piece-wise analytic data. II. The trace spaces and application to the boundary value problems with nonhomogeneous boundary conditions, SIAM J. Math. Anal. 20 (1989) 763-781.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 763-781
    • Babuška, I.1    Guo, B.Q.2
  • 7
    • 0030189240 scopus 로고    scopus 로고
    • Approximation properties of the h-p version of the finite element method
    • I. Babuška and B. Q. Guo, Approximation properties of the h-p version of the finite element method, Comput. Meth. Appl. Mech. Engrg. 133 (1996) 319-346.
    • (1996) Comput. Meth. Appl. Mech. Engrg. , vol.133 , pp. 319-346
    • Babuška, I.1    Guo, B.Q.2
  • 8
    • 84966243578 scopus 로고
    • Finite element-Galerkin approximation of the eigenvalues and eigenvectors of self-adjoint problems
    • I. Babuška and J. E. Osborn, Finite element-Galerkin approximation of the eigenvalues and eigenvectors of self-adjoint problems, Math. Comp. 52 (1989) 275-297.
    • (1989) Math. Comp. , vol.52 , pp. 275-297
    • Babuška, I.1    Osborn, J.E.2
  • 9
    • 0025448211 scopus 로고
    • The p- And h-p versions of the finite element method, an overview
    • I. Babuška and M. Suri, The p- and h-p versions of the finite element method, an overview, Comput. Meth. Appl. Mech. Engrg. 80 (1990) 5-26.
    • (1990) Comput. Meth. Appl. Mech. Engrg. , vol.80 , pp. 5-26
    • Babuška, I.1    Suri, M.2
  • 10
    • 0028734274 scopus 로고
    • The p- And h-p versions of the finite element method, basic principles and properties
    • I. Babuška and M. Suri, The p- and h-p versions of the finite element method, basic principles and properties, SIAM Rev. 36 (1994) 578-632.
    • (1994) SIAM Rev. , vol.36 , pp. 578-632
    • Babuška, I.1    Suri, M.2
  • 11
    • 0001878229 scopus 로고
    • 2-theory of the Maxwell operator in arbitrary domains
    • 2-theory of the Maxwell operator in arbitrary domains, Russ. Math. Surv. 42 (1987) 75-96.
    • (1987) Russ. Math. Surv. , vol.42 , pp. 75-96
    • Birman, M.1    Solomyak, M.2
  • 12
    • 0000999737 scopus 로고
    • On the main singularities of the electric component of the electro-magnetic field in regions with screens
    • M. Birman and M. Solomyak, On the main singularities of the electric component of the electro-magnetic field in regions with screens, St. Petersbg. Math. J. 5 (1993) 125-139.
    • (1993) St. Petersbg. Math. J. , vol.5 , pp. 125-139
    • Birman, M.1    Solomyak, M.2
  • 13
    • 17144426354 scopus 로고    scopus 로고
    • Discrete compactness for the hp version of rectangular edge finite elements
    • The University of Texas at Austin
    • D. Boffi, M. Costabel, M. Dauge and L. Demkowicz, Discrete compactness for the hp version of rectangular edge finite elements, ICES Report 04-29, The University of Texas at Austin, 2004.
    • (2004) ICES Report , vol.4 , Issue.29
    • Boffi, D.1    Costabel, M.2    Dauge, M.3    Demkowicz, L.4
  • 14
    • 0346902060 scopus 로고    scopus 로고
    • Discrete compactness for p and hp 2d edge finite elements
    • D. Boffi, L. Demkowicz and M. Costabel, Discrete compactness for p and hp 2d edge finite elements, Math. Mod. Meth. Appl. Sci. 13 (2003) 1673-1687.
    • (2003) Math. Mod. Meth. Appl. Sci. , vol.13 , pp. 1673-1687
    • Boffi, D.1    Demkowicz, L.2    Costabel, M.3
  • 15
    • 0001062958 scopus 로고
    • Régularité Gevrey pour le problème de Dirichlet dans des domaines à singularités coniques
    • P. Bolley, J. Camus and M. Dauge, Régularité Gevrey pour le problème de Dirichlet dans des domaines à singularités coniques, Comm. Partial Diff. Eqns. 10 (1985) 391-432.
    • (1985) Comm. Partial Diff. Eqns. , vol.10 , pp. 391-432
    • Bolley, P.1    Camus, J.2    Dauge, M.3
  • 17
    • 0038052997 scopus 로고    scopus 로고
    • Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron
    • A. Buffa, M. Costabel and M. Dauge, Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron, C. R. Acad. Sc. Paris, Série I 336 (2003) 565-570.
    • (2003) C. R. Acad. Sc. Paris, Série I , vol.336 , pp. 565-570
    • Buffa, A.1    Costabel, M.2    Dauge, M.3
  • 18
    • 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) 527-541.
    • (1991) J. Math. Anal. Appl. , vol.157 , pp. 527-541
    • Costabel, M.1
  • 19
    • 0033078434 scopus 로고    scopus 로고
    • Maxwell and Lamé eigenvalues on polyhedra
    • M. Costabel and M. Dauge, Maxwell and Lamé eigenvalues on polyhedra, Math. Meth. Appl. Sci. 22 (1999) 243-258.
    • (1999) Math. Meth. Appl. Sci. , vol.22 , pp. 243-258
    • Costabel, M.1    Dauge, M.2
  • 20
    • 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. Rational Mech. Anal. 151 (2000) 221-276.
    • (2000) Arch. Rational Mech. Anal. , vol.151 , pp. 221-276
    • Costabel, M.1    Dauge, M.2
  • 21
    • 0036912227 scopus 로고    scopus 로고
    • Weighted regularization of Maxwell equations in polyhedral domains
    • M. Costabel and M. Dauge, Weighted regularization of Maxwell equations in polyhedral domains, Numer. Math. 93 (2002) 239-277.
    • (2002) Numer. Math. , vol.93 , pp. 239-277
    • Costabel, M.1    Dauge, M.2
  • 23
    • 17144387416 scopus 로고    scopus 로고
    • Weighted regularization of Maxwell equations - Computations in curvilinear polygons
    • editors, Ischia, July 2001, eds. F. Brezzi, A. Buffa, S. Corsaro and A. Murli (Springer)
    • M. Costabel, M. Dauge, D. Martin and G. Vial, Weighted regularization of Maxwell equations - computations in curvilinear polygons, in editors, Proc. of the 4th European Conf. on Numerical Mathematics and Advanced Applications, Ischia, July 2001, eds. F. Brezzi, A. Buffa, S. Corsaro and A. Murli (Springer, 2002), pp. 273-280.
    • (2002) Proc. of the 4th European Conf. on Numerical Mathematics and Advanced Applications , pp. 273-280
    • Costabel, M.1    Dauge, M.2    Martin, D.3    Vial, G.4
  • 26
    • 0036758116 scopus 로고    scopus 로고
    • Concepts - An object-oriented software package for partial differential equations
    • P. Frauenfelder and C. Lage, Concepts - an object-oriented software package for partial differential equations, Math. Mod. Numer. Anal. 36 (2002) 937-951.
    • (2002) Math. Mod. Numer. Anal. , vol.36 , pp. 937-951
    • Frauenfelder, P.1    Lage, C.2
  • 27
    • 21444453590 scopus 로고    scopus 로고
    • 3. I. Countably normed spaces on polyhedral domains
    • 3. I. Countably normed spaces on polyhedral domains, Proc. Roy. Soc. Edinburgh Sec. A127 (1997) 77-126.
    • (1997) Proc. Roy. Soc. Edinburgh Sec. , vol.A127 , pp. 77-126
    • Guo, B.1    Babuška, I.2
  • 29
    • 0002898475 scopus 로고
    • The h-p version of the finite element method for elliptic equations of order 2m
    • B. Q. Guo, The h-p version of the finite element method for elliptic equations of order 2m, Numer. Math. 53 (1988) 199-224.
    • (1988) Numer. Math. , vol.53 , pp. 199-224
    • Guo, B.Q.1
  • 30
    • 85095827382 scopus 로고    scopus 로고
    • Finite elements in computational electromagnetism
    • R. Hiptmair, Finite elements in computational electromagnetism, Acta Numer. 11 (2002) 237-339.
    • (2002) Acta Numer. , vol.11 , pp. 237-339
    • Hiptmair, R.1
  • 31
    • 0000309125 scopus 로고
    • Boundary-value problems for elliptic equations in domains with conical or angular points
    • V. A. Kondrat'ev, Boundary-value problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc. 16 (1967) 227-313.
    • (1967) Trans. Moscow Math. Soc. , vol.16 , pp. 227-313
    • Kondrat'Ev, V.A.1
  • 32
    • 17144411746 scopus 로고    scopus 로고
    • Online documentation
    • D. Martin, Mélina, Online documentation: http://perso.univ- rennesl.fr/daniel.martin/melina.
    • Mélina
    • Martin, D.1
  • 33
    • 0037049917 scopus 로고    scopus 로고
    • An hp-adaptive finite element method for electro-magnetics. II. A 3D implementation
    • W. Rachowicz and L. Demkowicz, An hp-adaptive finite element method for electro-magnetics. II. A 3D implementation, Internat. J. Numer. Meth. Engrg. 53 (2002) 147-180.
    • (2002) Internat. J. Numer. Meth. Engrg. , vol.53 , pp. 147-180
    • Rachowicz, W.1    Demkowicz, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.