On a hierarchical basis multilevel method with nonconforming P1 elements
type: Item
instance of: scholarly article
title: On a hierarchical basis multilevel method with nonconforming P1 elements
zbMATH Open document ID: 0767.65078
DOI: 10.1007/BF01396226
published in: Numerische Mathematik
publication date: 1993-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/133648
review text: The paper extends \textit{H. Yserentant}'s hierarchical basis multilevel method [ibid. 49, 379-412 (1986; Zbl 0608.65065)] to second order elliptic boundary value problems discretized by nonconforming \(P1\) triangular (Crouseiz-Raviart) elements. The method is based on the sequence of finite element subspaces \(S_ 0,\dots,S_ K=S\) which correspond to a successive refinement. On the contrary to the conforming case, these finite element subspaces are not nested. This difficulty is overcome by introducing intergrid transfer operators. Thorough analysis of these operators and their norms is important for deriving the main result: The condition number of the hierarchical discretization matrix is bounded by \(O(k)\) where \(k\) is the number of refinement levels. Note that this result is better than the corresponding result for conforming \(P1\) elements which is \(O(k^ 2)\). These results are supported by numerical experiments.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 118306
zbMATH Keywords: nonconforming \(P1\) triangular elements
zbMATH Keywords: hierarchical basis multilevel method
zbMATH Keywords: second order elliptic boundary value problems
zbMATH Keywords: finite element
zbMATH Keywords: condition number
zbMATH Keywords: numerical experiments
author: Peter Oswald
reviewed by: R. Blaheta
MaRDI profile type: Publication
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OpenAlex ID: W2022663709
description: scientific article; zbMATH DE number 118306