The discrete compactness property for anisotropic edge elements on polyhedral domains
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 grad...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
2013
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | 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. |
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| Bibliografía: | 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 |
| ISSN: | 0764583X |
| DOI: | 10.1051/m2an/2012024 |