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Abstract:

We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl. Sci. 21 (1998) 519—549]. They are appropriately graded near singular corners and edges of the polyhedron. © EDP Sciences, SMAI 2013.

Registro:

Documento: Artículo
Título:The discrete compactness property for anisotropic edge elements on polyhedral domains
Autor:Lombardi, A.L.
Filiación:Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Provincia de Buenos Airesn, Los Polvorines, B1613 GSX, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Member of CONICET, Argentina
Palabras clave:Anisotropic finite elements; Discrete compactness property; Edge elements; Maxwell equations
Año:2013
Volumen:47
Número:1
Página de inicio:169
Página de fin:181
DOI: http://dx.doi.org/10.1051/m2an/2012024
Título revista:Mathematical Modelling and Numerical Analysis
Título revista abreviado:Math. Model. Numer. Anal.
ISSN:0764583X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0764583X_v47_n1_p169_Lombardi

Referencias:

  • Apel, T., Nicaise, S., The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges (1998) Math. Meth. Appl. Sci., 21, pp. 519-549
  • Boffi, D., Fortin operator and discrete compactness for edge elements (2000) Numer. Math., 87, pp. 229-246
  • Boffi, D., Finite element approximation of eigenvalue problems (2010) Acta Numer, 19, pp. 1-120
  • Buffa, A., Costabel, M., Dauge, M., Algebraic convergence for anisotropic edge elements in polyhedral domains (2005) Numer. Math., 101, pp. 29-65
  • Caorsi, S., Fernandes, P., Raffetto, M., On the convergence of Galerkin finite element approximations of electromagnetic eigenproblems (2000) SIAM J. Numer. Anal., 38, pp. 580-607
  • Caorsi, S., Fernandes, P., Raffetto, M., Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements (2001) Math. Model. Numer. Anal., 35, pp. 331-354
  • Girault, V., Raviart, P.A., Finite Element Methods for Navier-Stokes Equations (1986) Theory and Applications., , SpringerVerlag, Berlin
  • Hiptmair, R., Finite elements in computational electromagnetism (2002) Acta Numer, 11, pp. 237-339
  • Kikuchi, F., On a discrete compactness property for the Nedelec finite elements (1989) J. Fac. Sci. Univ. Tokyo Sect. IA Math., 36, pp. 479-490
  • Krizek, M., On the maximum angle condition for linear tetrahedral elements (1992) SIAM J. Numer. Anal., 29, pp. 513-520
  • Leis, R., (1986) Initial Boundary Value Problems in Mathematical Physics, , John Wiley, New York
  • Lombardi, A.L., Interpolation error estimates for edge elements on anisotropic meshes (2011) IMA J. Numer. Anal, 31, pp. 1683-1712
  • Monk, P., (2003) Finite Element Methods for Maxwell’s Equations, , Oxford University Press, New York
  • Monk, P., Demkowicz, L., Discrete compactness and the approximation of Maxwell’s equations in R3 (2001) Math. Comp., 70, pp. 507-523
  • Nedelec, J.C., Mixed finite elements in R3 (1980) Numer. Math., 35, pp. 315-341
  • Nicaise, S., Edge elements on anisotropic meshes and approximation of the Maxwell equations (2001) SIAM J. Numer. Anal., 39, pp. 784-816
  • Raviart, P.A., Thomas, J.-M., A mixed finite element method for second order elliptic problems (1977) Mathematical Aspects of the Finite Element Method, , edited by I. Galligani and E. Magenes
  • Weber, C.H., A local compactness theorem for Maxwell’s equations (1980) Math. Meth. Appl. Sci., 2, pp. 12-25

Citas:

---------- APA ----------
(2013) . The discrete compactness property for anisotropic edge elements on polyhedral domains. Mathematical Modelling and Numerical Analysis, 47(1), 169-181.
http://dx.doi.org/10.1051/m2an/2012024
---------- CHICAGO ----------
Lombardi, A.L. "The discrete compactness property for anisotropic edge elements on polyhedral domains" . Mathematical Modelling and Numerical Analysis 47, no. 1 (2013) : 169-181.
http://dx.doi.org/10.1051/m2an/2012024
---------- MLA ----------
Lombardi, A.L. "The discrete compactness property for anisotropic edge elements on polyhedral domains" . Mathematical Modelling and Numerical Analysis, vol. 47, no. 1, 2013, pp. 169-181.
http://dx.doi.org/10.1051/m2an/2012024
---------- VANCOUVER ----------
Lombardi, A.L. The discrete compactness property for anisotropic edge elements on polyhedral domains. Math. Model. Numer. Anal. 2013;47(1):169-181.
http://dx.doi.org/10.1051/m2an/2012024