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

Bärbel Janssen, Guido Kanschat

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)2095-2114
Number of pages20
JournalSIAM Journal on Scientific Computing
Volume33
Issue number4
DOIs
StatePublished - Jan 2011
Externally publishedYes

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