Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methods

Handle URI:
http://hdl.handle.net/10754/597458
Title:
Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methods
Authors:
Janssen, Bärbel; Kanschat, Guido
Abstract:
A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method's convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. © 2011 Societ y for Industrial and Applied Mathematics.
Citation:
Janssen B, Kanschat G (2011) Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methods. SIAM Journal on Scientific Computing 33: 2095–2114. Available: http://dx.doi.org/10.1137/090778523.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jan-2011
DOI:
10.1137/090778523
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This author's work was supported by the German Research Association (DFG) and the International Graduate College IGK 710.This author's work was supported by the National Science Foundation under grants DMS-0713829 and DMS-0810387 and by the King Abdullah University of Science and Technology (KAUST) through award KUS-C1-016-04. Some of the experiments were performed during a visit to the Institute of Mathematics and its Applications in Minneapolis.
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Full metadata record

DC FieldValue Language
dc.contributor.authorJanssen, Bärbelen
dc.contributor.authorKanschat, Guidoen
dc.date.accessioned2016-02-25T12:40:08Zen
dc.date.available2016-02-25T12:40:08Zen
dc.date.issued2011-01en
dc.identifier.citationJanssen B, Kanschat G (2011) Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methods. SIAM Journal on Scientific Computing 33: 2095–2114. Available: http://dx.doi.org/10.1137/090778523.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/090778523en
dc.identifier.urihttp://hdl.handle.net/10754/597458en
dc.description.abstractA multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method's convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. © 2011 Societ y for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis author's work was supported by the German Research Association (DFG) and the International Graduate College IGK 710.This author's work was supported by the National Science Foundation under grants DMS-0713829 and DMS-0810387 and by the King Abdullah University of Science and Technology (KAUST) through award KUS-C1-016-04. Some of the experiments were performed during a visit to the Institute of Mathematics and its Applications in Minneapolis.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAdaptive mesh refinementen
dc.subjectFinite element methoden
dc.subjectHanging nodesen
dc.subjectMaxwell equationsen
dc.subjectMultigrid methodsen
dc.titleAdaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methodsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversitat Heidelberg, Heidelberg, Germanyen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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