JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (4): 40-48.doi: 10.6040/j.issn.1671-9352.0.2022.280

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Cubic B-spline finite element method for parabolic optimal control problems

DU Fang-fang, SUN Tong-jun*   

  1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Published:2023-03-27

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Abstract: A cubic B-spline finite element method is proposed for optimal control problems governed by a class of fourth-order nonlinear parabolic equations. The state and co-state variables are discretized by piecewise cubic B-spline continuous functions which have better smoothness and the control variable is approximated by piecewise constant functions. The numerical solutions of the state and co-state variables thus obtained are second-order continuously differentiable. A fully discrete scheme of the optimality system is established and solved by an iterative method. Finally, some numerical examples are presented to verify the effectivity of the proposed method.

Key words: cubic B-spline finite element method, optimal control problem, fourth-order nonlinear parabolic equation, optimality system, iterative method

CLC Number: 

  • O241.82
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