A bicubic B-spline finite element method for fourth-order semilinear parabolic optimal control problems
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 co-state 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.