A new a priori error estimate of nonconforming finite element methods

Jun Hu, Rui Ma*, Zhong Ci Shi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

This paper is devoted to a new error analysis of nonconforming finite element methods. Compared with the classic error analysis in literature, only weak continuity, the F-E-M-Test for nonconforming finite element spaces, and basic H m regularity for exact solutions of 2m-th order elliptic problems under consideration are assumed. The analysis is motivated by ideas from a posteriori error estimates and projection average operators. One main ingredient is a novel decomposition for some key average terms on (n - 1)-dimensional faces by introducing a piecewise constant projection, which defines the generalization to more general nonconforming finite elements of the results in literature. The analysis and results herein are conjectured to apply for all nonconforming finite elements in literature.

Original languageEnglish
Pages (from-to)887-902
Number of pages16
JournalScience China Mathematics
Volume57
Issue number5
DOIs
Publication statusPublished - May 2014
Externally publishedYes

Keywords

  • consistency error
  • error estimate
  • nonconforming finite element

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Hu, J., Ma, R., & Shi, Z. C. (2014). A new a priori error estimate of nonconforming finite element methods. Science China Mathematics, 57(5), 887-902. https://doi.org/10.1007/s11425-014-4793-3