Goal-oriented adaptive method for Fredholm partial integro-differential equations

被引:3
|
作者
Sameeh, M. [1 ]
Elsaid, A. [1 ,2 ]
El-Agamy, M. [1 ,3 ]
机构
[1] Mansoura Univ, Fac Engn, Math & Engn Phys Dept, Mansoura, Egypt
[2] Egypt Japan Univ Sci & Technol E JUST, Inst Basic & Appl Sci, Dept Math, Alexandria, Egypt
[3] German Int Univ GIU, Dept Math, Cairo, Egypt
关键词
Finite element method; Recovery techniques; Goal-oriented error; Adaptive refinement; SUPERCONVERGENT PATCH RECOVERY; POSTERIORI ERROR ESTIMATION; FINITE-ELEMENT-ANALYSIS; INTEGRAL-EQUATIONS; NUMERICAL-SOLUTION; BERNSTEIN POLYNOMIALS; GALERKIN; SIMULATION; SYSTEM; ORDER;
D O I
10.1016/j.asej.2023.102541
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this article, a goal-oriented adaptive scheme is proposed for Fredholm partial integro-differential equations (FPIDEs). The aim of this work is to obtain higher accuracy approximations for the unknown function and its derivative at a given fixed point. In the proposed goal-oriented scheme, as opposed to the typical energy norm, the finite element approximated error is computed based on the quantities of interest. These designated quantities are identified by linear goal functions. The formula of the goal error and the a priori estimate of its upper bound are derived. An a posteriori error estimate is formulated and then approximated by using the recovered gradient. Some numerical tests are presented to show the efficiency of the proposed scheme in hastening the achievement of regional aspects of the solution.
引用
收藏
页数:7
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