Neumann–Neumann algorithms for a mortar Crouzeix–Raviart element for 2nd order elliptic problems

The paper proposes two scalable variants of the Neumann–Neumann algorithm for the lowest order Crouzeix–Raviart finite element or the nonconforming P 1 finite element on nonmatching meshes. The overall discretization is done using a mortar technique which is based on the application of an approximat...

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Veröffentlicht in:BIT (Nordisk Tidskrift for Informationsbehandling) Jg. 48; H. 3; S. 607 - 626
Hauptverfasser: Marcinkowski, L., Rahman, T.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Netherlands 01.09.2008
Springer
Schlagworte:
Computational Mathematics and Numerical Analysis
Exact sciences and technology
Mathematics
Mathematics and Statistics
Numeric Computing
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Domain Decomposition Method
Mortar Method
Nonconforming Element
Slave Side
Master Side
Grid pattern
Neumann-Neumann method. 65F10
Non conforming finite element
Crouzeix-Raviart FE
Algorithm
Partial differential equation
Discretization method
Convergence
Finite element method
Numerical analysis
Elliptic equation
mortar method
65N55
65N30
ISSN:0006-3835, 1572-9125
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:The paper proposes two scalable variants of the Neumann–Neumann algorithm for the lowest order Crouzeix–Raviart finite element or the nonconforming P 1 finite element on nonmatching meshes. The overall discretization is done using a mortar technique which is based on the application of an approximate matching condition for the discrete functions, requiring function values only at the mesh interface nodes. The algorithms are analyzed using the abstract Schwarz framework, proving a convergence which is independent of the jumps in the coefficients of the problem and only depends logarithmically on the ratio between the subdomain size and the mesh size.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-008-0167-y