平面弹性柯西问题的一种数值解法

A Numerical Method for a Cauchy Problem for Plane Elasticity

利用最优控制方法和Tikhonov正则化方法导出了求解平面弹性柯西问题的一种数值方法.在连续情形,证明了正则化解在L2(Γid)范数下的收敛性,并给出了在一种弱范数下的误差估计.通过有限元方法得到离散化极小化问题,同时证明了有限元解的收敛性.数值算例验证了该方法的有效性.

A numerical method was proposed for solving a Cauchy problem about plane elasticity, based on an optimal control approach coupled with the Tikhonov regularization. In the continuous case, a convergence property in the L2 （Fid） norm and an error bound in some weak norm were derived for the regularized solution. A discretization method for the continuous problem was presented by the finite element method, and its convergence property was also discussed. Some numerical examples were reported to illustrate the computational performance of the method proposed.