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Optimal estimates for lower and upper bounds of approximation errors in the p-version of the finite element method in two dimensions

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Summary. This paper will analyze the lower and upper error bounds of the finite element solution of the p-version for linear elliptic problems in polygonal domains. The optimal rate of convergence is rigorously proved based on the sharp estimates of lower and upper bounds of the approximation error.

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Authors and Affiliations

  1. Texas Institute for Computational and Applied Mathematics, University of Texas, Austin, TX 78712, USA , , , , , , US

    Ivo BabuškaRID="*"ID="*" Partially supported by the US office of Naval Research under Grant N00014-90-J-1030 and National Science Foundation under grant DMJ-95-01841 & Benqi GuoRID="**"ID="**" Partially supported by National Science and Engineering on Research Council of Canada under Grant OGP0046726 and by Research Fellowship of TICAM, University of Texas at Austin during his stay (1996–1997).

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  1. Ivo BabuškaRID="*"ID="*" Partially supported by the US office of Naval Research under Grant N00014-90-J-1030 and National Science Foundation under grant DMJ-95-01841
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  2. Benqi GuoRID="**"ID="**" Partially supported by National Science and Engineering on Research Council of Canada under Grant OGP0046726 and by Research Fellowship of TICAM, University of Texas at Austin during his stay (1996–1997).
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Received October 14, 1997 / Revised version received April 8, 1999 / Published online February 17, 2000

RID="*"

ID="*" Partially supported by the US office of Naval Research under Grant N00014-90-J-1030 and National Science Foundation under grant DMJ-95-01841

RID="**"

ID="**" Partially supported by National Science and Engineering on Research Council of Canada under Grant OGP0046726 and by Research Fellowship of TICAM, University of Texas at Austin during his stay (1996–1997).

RID=""

ID="" <E5>Dedicated to Prof. O. Widlund on the occasion of his 60th birthday</E5>

RID=""

ID=""<E5>Correspondence to:</E5> B. Guo

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BabuškaRID="*"ID="*" Partially supported by the US office of Naval Research under Grant N00014-90-J-1030 and National Science Foundation under grant DMJ-95-01841, I., GuoRID="**"ID="**" Partially supported by National Science and Engineering on Research Council of Canada under Grant OGP0046726 and by Research Fellowship of TICAM, University of Texas at Austin during his stay (1996&ndash;1997)., B. Optimal estimates for lower and upper bounds of approximation errors in the p-version of the finite element method in two dimensions. Numer. Math. 85, 219–255 (2000). https://doi.org/10.1007/PL00005387

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  • DOI: https://doi.org/10.1007/PL00005387

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