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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2013
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| 005 | 20230518204314.0 | ||
| 008 | 190411s2013 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84996129286 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Lombardi, A.L. | |
| 245 | 1 | 4 | |a The discrete compactness property for anisotropic edge elements on polyhedral domains |
| 260 | |c 2013 | ||
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a 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 | ||
| 504 | |a Boffi, D., Fortin operator and discrete compactness for edge elements (2000) Numer. Math., 87, pp. 229-246 | ||
| 504 | |a Boffi, D., Finite element approximation of eigenvalue problems (2010) Acta Numer, 19, pp. 1-120 | ||
| 504 | |a Buffa, A., Costabel, M., Dauge, M., Algebraic convergence for anisotropic edge elements in polyhedral domains (2005) Numer. Math., 101, pp. 29-65 | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a Girault, V., Raviart, P.A., Finite Element Methods for Navier-Stokes Equations (1986) Theory and Applications., , SpringerVerlag, Berlin | ||
| 504 | |a Hiptmair, R., Finite elements in computational electromagnetism (2002) Acta Numer, 11, pp. 237-339 | ||
| 504 | |a 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 | ||
| 504 | |a Krizek, M., On the maximum angle condition for linear tetrahedral elements (1992) SIAM J. Numer. Anal., 29, pp. 513-520 | ||
| 504 | |a Leis, R., (1986) Initial Boundary Value Problems in Mathematical Physics, , John Wiley, New York | ||
| 504 | |a Lombardi, A.L., Interpolation error estimates for edge elements on anisotropic meshes (2011) IMA J. Numer. Anal, 31, pp. 1683-1712 | ||
| 504 | |a Monk, P., (2003) Finite Element Methods for Maxwell’s Equations, , Oxford University Press, New York | ||
| 504 | |a Monk, P., Demkowicz, L., Discrete compactness and the approximation of Maxwell’s equations in R3 (2001) Math. Comp., 70, pp. 507-523 | ||
| 504 | |a Nedelec, J.C., Mixed finite elements in R3 (1980) Numer. Math., 35, pp. 315-341 | ||
| 504 | |a Nicaise, S., Edge elements on anisotropic meshes and approximation of the Maxwell equations (2001) SIAM J. Numer. Anal., 39, pp. 784-816 | ||
| 504 | |a 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 | ||
| 504 | |a Weber, C.H., A local compactness theorem for Maxwell’s equations (1980) Math. Meth. Appl. Sci., 2, pp. 12-25 | ||
| 520 | 3 | |a 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. |l eng | |
| 593 | |a Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Provincia de Buenos Airesn, Los Polvorines, B1613 GSX, Argentina | ||
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Member of CONICET, Argentina | ||
| 690 | 1 | 0 | |a ANISOTROPIC FINITE ELEMENTS |
| 690 | 1 | 0 | |a DISCRETE COMPACTNESS PROPERTY |
| 690 | 1 | 0 | |a EDGE ELEMENTS |
| 690 | 1 | 0 | |a MAXWELL EQUATIONS |
| 773 | 0 | |d 2013 |g v. 47 |h pp. 169-181 |k n. 1 |p Math. Model. Numer. Anal. |x 0764583X |w (AR-BaUEN)CENRE-1603 |t Mathematical Modelling and Numerical Analysis | |
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| 856 | 4 | 0 | |u https://doi.org/10.1051/m2an/2012024 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_0764583X_v47_n1_p169_Lombardi |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0764583X_v47_n1_p169_Lombardi |y Registro en la Biblioteca Digital |
| 961 | |a paper_0764583X_v47_n1_p169_Lombardi |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 73959 | ||