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Numerical Algorithms

, Volume 80, Issue 2, pp 429–445 | Cite as

A two-grid parallel partition of unity finite element scheme

  • Guangzhi DuEmail author
  • Liyun Zuo
Original Paper
  • 19 Downloads

Abstract

A two-grid parallel partition of unity finite element scheme is proposed and analyzed in this paper for linear elliptic boundary value problems. The interesting features of this scheme contain the following: (1) a partition of unity is constructed to derive the globally continuous finite element solution; (2) errors decay exponentially with patches of diameter kH increase; and (3) a global coarse grid correction is done to improve the L2 − accuracy of the approximation. Numerical experiments are presented at the end of the paper to support our analysis.

Keywords

Partition of unity Parallel algorithm Error estimates Finite element Two-grid method 

Mathematics Subject Classification (2010)

65N15 65N30 65N55 

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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsShandong Normal UniversityJinanChina
  2. 2.School of Mathematical SciencesUniversity of JinanJinanChina

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