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

doi:10.1007/s10473-024-0619-8

Abstract

Abstract: 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 co-state variables in two space dimensions. A Crank-Nicolson difference scheme is constructed for time discretization. The resulting numerical solutions belong to $C^2$ 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.

Key words: bicubic B-spline finite element method, optimal control problem, Bogner-Fox-Schmit element, Crank-Nicolson scheme, numerical experiment

CLC Number:

49K20

Fangfang DU, Tongjun SUN. A BICUBIC B-SPLINE FINITE ELEMENT METHOD FOR FOURTH-ORDER SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS[J].Acta mathematica scientia,Series B, 2024, 44(6): 2411-2421.

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