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01-09-2021 | Issue 3/2021

Calcolo 3/2021

Local ultraconvergence of quadratic element

Calcolo > Issue 3/2021
Wen-ming He, Ren Zhao
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Wen-ming He and Ren Zhao are co-first authors.

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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.

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