中文摘要：

考虑一类由椭圆性方程和热传导方程共同来刻画的准静态弹性模型，通过给定观测值来反演边界的牵引力。首先构造一个凸目标泛函，并引入Tikhonov正则化方法，使之极小化得到一个稳定的近似解。再用有限元离散求解，导出误差估计。最后，用数值例子说明算法的可行性和有效性。

英文摘要：

The quasistatic elastic problem is formulated as an elliptic system for the displace-ments coupled with a parabolic equation for the damage field. The corresponding inverse problem is reformulated as an optimal control problem to find a stable traction, by a given observation data. Firstly, a convex functional is constructed with Tikhonov regularization, and a stable approximation of surface traction is obtained by minimizing it. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. At last, a numerical algorithm is detailed and three examples illustrate the e-ciency of the algorithm.