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.
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
.
DOI: 10.1007/s10473-024-0619-8
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