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

被引：0
|
作者：
杜芳芳
孙同军
机构：
[1] SchoolofMathematics,ShandongUniversity
来源：
Acta Mathematica Scientia | 2024年 / 44卷 / 06期
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D O I：
暂无
中图分类号：
O232 [最优控制]; O241.82 [偏微分方程的数值解法];
学科分类号：
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 C2 in 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.
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页码：2411 / 2421
页数：11
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