Local ultraconvergence of quadratic element

The displacement and gradient of a finite element solution are of primary interest and a high accuracy displacement and gradient approximation are always desirable in scientific computing. In this paper, we introduce a new state of the art way to reconstruct a high accuracy approximated gradient. Th...

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Bibliographic Details
Published inCalcolo Vol. 58; no. 3
Main Authors He, Wen-ming, Zhao, Ren
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2021
Springer Nature B.V
Subjects
Accuracy
Approximation
Displacement
Interpolation
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Post-processing
Theory of Computation
Integral identity
The interpolation post-processing technique
Secondary 45N08
Quadratic triangular element
Primary 65N30
Ultraconvergence
The local symmetric technique
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Summary:The displacement and gradient of a finite element solution are of primary interest and a high accuracy displacement and gradient approximation are always desirable in scientific computing. In this paper, we introduce a new state of the art way to reconstruct a high accuracy approximated gradient. The proposed method inherits the advantages of both the extrapolation technique and the interpolation post-processing technique. We theoretically justify the fifth-order local ultraconvergence of the post-processing gradient. In the meanwhile, an ultraconvergent displacement can be obtained from this post-processing procedure. The theoretical result is numerically verified and validated.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-021-00427-4