An adaptive finite element method for Riesz fractional partial integro-differential equations

被引:8
作者
Adel, E. [1 ]
El-Kalla, I. L. [1 ]
Elsaid, A. [1 ,2 ]
Sameeh, M. [1 ]
机构
[1] Mansoura Univ, Fac Engn, Math & Engn Phys Dept, PO 35516, Mansoura, Egypt
[2] Egypt Japan Univ Sci & Technol E JUST, Inst Basic & Appl Sci, Dept Math, Alexandria, Egypt
关键词
Adaptive finite element method; Fractional partial integro-differential equation; Gradient recovery techniques; Riesz fractional derivative; Polynomial preserving recovery; SUPERCONVERGENT PATCH RECOVERY; ADVECTION-DISPERSION EQUATIONS; POSTERIORI ERROR ESTIMATORS; NUMERICAL APPROXIMATION; BOUNDED DOMAINS; SPECTRAL METHOD; WAVE-EQUATION; DIFFUSION; SPACE; GRADIENT;
D O I
10.1007/s40096-023-00518-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Riesz fractional derivative has been employed to describe the spatial derivative in a variety of mathematical models. In this work, the accuracy of the finite element method (FEM) approximations to Riesz fractional derivative was enhanced by using adaptive refinement. This was accomplished by deducing the Riesz derivatives of the FEM bases to work on non-uniform meshes. We utilized these derivatives to recover the gradient in a space fractional partial integro-differential equation in the Riesz sense. The recovered gradient was used as an a posteriori error estimator to control the adaptive refinement scheme. The stability and the error estimate for the proposed scheme are introduced. The results of some numerical examples that we carried out illustrate the improvement in the performance of the adaptive technique.
引用
收藏
页码:611 / 624
页数:14
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