University of Leicester
Browse
Dong2018_Article_OnTheExPonentOfExPonentialConv.pdf (803.14 kB)

On the exponent of exponential convergence of p-version FEM spaces

Download (803.14 kB)
journal contribution
posted on 2019-01-15, 12:05 authored by Zhaonan Dong
We study the exponent of the exponential rate of convergence in terms of the number of degrees of freedom for various non-standard p-version finite element spaces employing reduced cardinality basis. More specifically, we show that serendipity finite element methods and discontinuous Galerkin finite element methods with total degree Pp basis have a faster exponential convergence with respect to the number of degrees of freedom than their counterparts employing the tensor product Qp basis for quadrilateral/hexahedral elements, for piecewise analytic problems under p-refinement. The above results are proven by using a new p-optimal error bound for the L2-orthogonal projection onto the total degree Pp basis, and for the H1- projection onto the serendipity finite element space over tensor product elements with dimension d ≥ 2. These new p-optimal error bounds lead to a larger exponent of the exponential rate of convergence with respect to the number of degrees of freedom. Moreover, these results show that part of the basis functions in Qp basis plays no roles in achieving the hp-optimal error bound in the Sobolev space. The sharpness of theoretical results is also verified by a series of numerical examples.

Funding

Z. D. was supported by the Leverhulme Trust (grant no. RPG-2015-306).

History

Citation

Advances in Computational Mathematics, 2018

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • VoR (Version of Record)

Published in

Advances in Computational Mathematics

Publisher

Springer (part of Springer Nature)

issn

1019-7168

eissn

1572-9044

Acceptance date

2018-09-16

Copyright date

2018

Available date

2019-01-15

Publisher version

https://link.springer.com/article/10.1007/s10444-018-9637-1

Notes

Mathematics Subject Classification (2010) 65N30 65N15 65N50

Language

en

Usage metrics

    University of Leicester Publications

    Categories

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC