A BICUBIC B-SPLINE FINITE ELEMENT METHOD FOR FOURTH-ORDER SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS  

作　　者：Fangfang DU Tongjun SUN 杜芳芳;孙同军(School of Mathematics,Shandong University,Jinan 250100,China)

机构地区：[1]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Acta Mathematica Scientia》2024年第6期2411-2421,共11页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11871312,12131014);the Natural Science Foundation of Shandong Province,China(ZR2023MA086)。

摘　　要：A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.

关 键 词：bicubic B-spline finite element method optimal control problem Bogner-Fox-Schmit element Crank-Nicolson scheme numerical experiment 

分 类 号：O232[理学—运筹学与控制论] O241.82[理学—数学]