TY - JOUR
T1 - Approximation of eigenvalues in mixed form, Discrete Compactness Property, and application to hp mixed finite elements
AU - Boffi, Daniele
N1 - Generated from Scopus record by KAUST IRTS on 2020-05-05
PY - 2007/8/1
Y1 - 2007/8/1
N2 - In this paper we discuss the Discrete Compactness Property (DCP) which is a well-known tool for the analysis of finite element approximations of Maxwell's eigenvalues. We restrict our presentation to Maxwell's eigenvalues, but the theory applies to more general situations and in particular to mixed finite element schemes that can be written in the framework of de Rham complex and which enjoy suitable compactness properties. We investigate the relationships between DCP and standard mixed conditions for the good approximation of eigenvalues. As a consequence of our theory, the convergence analysis of the rectangular hp version of Raviart-Thomas finite elements for the approximation of Laplace eigenvalues is presented as a corollary of the analogous result for hp edge elements applied to the approximation of Maxwell's eigenvalues [D. Boffi, M. Costabel, M. Dauge, L. Demkowicz, Discrete compactness for the hp version of rectangular edge finite elements, SIAM J. Numer. Anal. 44 (3) (2006) 979-1004]. © 2007 Elsevier B.V. All rights reserved.
AB - In this paper we discuss the Discrete Compactness Property (DCP) which is a well-known tool for the analysis of finite element approximations of Maxwell's eigenvalues. We restrict our presentation to Maxwell's eigenvalues, but the theory applies to more general situations and in particular to mixed finite element schemes that can be written in the framework of de Rham complex and which enjoy suitable compactness properties. We investigate the relationships between DCP and standard mixed conditions for the good approximation of eigenvalues. As a consequence of our theory, the convergence analysis of the rectangular hp version of Raviart-Thomas finite elements for the approximation of Laplace eigenvalues is presented as a corollary of the analogous result for hp edge elements applied to the approximation of Maxwell's eigenvalues [D. Boffi, M. Costabel, M. Dauge, L. Demkowicz, Discrete compactness for the hp version of rectangular edge finite elements, SIAM J. Numer. Anal. 44 (3) (2006) 979-1004]. © 2007 Elsevier B.V. All rights reserved.
UR - https://linkinghub.elsevier.com/retrieve/pii/S0045782507000953
UR - http://www.scopus.com/inward/record.url?scp=34447096192&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2006.10.024
DO - 10.1016/j.cma.2006.10.024
M3 - Article
SN - 0045-7825
VL - 196
SP - 3672
EP - 3681
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 37-40 SPEC. ISS.
ER -