论文标题
部分可观测时空混沌系统的无模型预测
Unique continuation for the Lamé system using stabilized finite element methods
论文作者
论文摘要
我们引入了一种任意秩序，稳定的有限元方法，用于解决具有带有可变系数的时谐弹性波方程的唯一延续问题。根据条件稳定性估计，我们证明了所提出的方法的收敛速率，该方法考虑了噪声水平和多项式程度。一系列数值实验证实了我们的理论结果，并探讨了其他方面，例如重建的质量如何取决于相关域的几何形状。我们发现某些凸性特性对于获得数据域以外的波位移的良好恢复至关重要，并且较高的多项式顺序可以更有效，但对问题的条件性质不良，也更敏感。
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove convergence rates for the proposed method which take into account the noise level and the polynomial degree. A series of numerical experiments corroborates our theoretical results and explores additional aspects, e.g. how the quality of the reconstruction depends on the geometry of the involved domains. We find that certain convexity properties are crucial to obtain a good recovery of the wave displacement outside the data domain and that higher polynomial orders can be more efficient but also more sensitive to the ill-conditioned nature of the problem.
