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

作　　者：黄学海[1] 黄建国[1,2] 陈宇[1] 

机构地区：[1]上海交通大学数学系,上海200240 [2]上海师范大学上海高校计算科学E-研究院,上海200234

出　　处：《上海交通大学学报》2009年第8期1350-1356,共7页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金资助项目(10771138);上海高校计算科学E-研究院特聘研究员经费项目(E03004)

摘　　要：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.

关 键 词：柯西问题 最优控制 TIKHONOV正则化 有限元方法 

分 类 号：O241.82[理学—计算数学]