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Local ultraconvergence of high order finite element method by interpolation postprocessing technique for elliptic problems with constant coefficients
Computers & Mathematics with Applications ( IF 2.811 ) Pub Date : 2019-12-09 , DOI: 10.1016/j.camwa.2019.11.016
Wenming He; Xiong Liu; Jin Xiao

Assume that u(x) satisfies the problem Lu(x)≡−∂∂xi(aij∂u∂xj)=f(x),∀x∈Ω,u(x)=0,∀x∈∂Ω. In this article, using interpolation postprocessing technique, we will investigate the local ultraconvergence of the primal variable and the derivative of finite element approximation of u(x) using piecewise polynomials of degrees bi-k(k≥3) over a rectangular partition. Assume that k≥3 is odd and x0 is an interior vertex satisfying ρ(x0,∂Ω)≥c. Using the new interpolation postprocessing formula presented in this study, we show that the primal variable and the derivative of the post-processed finite element solution using piecewise of degrees bi-k(k≥3) at x0 converge to the primal variable and the derivative of the exact solution with order O(hk+3|lnh|) under suitable regularity and mesh conditions, respectively. Finally, we use numerical experiments to illustrate our theoretical findings.
更新日期:2020-03-24

 

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