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.
翻译:根据有条件的稳定估计,我们证明考虑到噪音水平和多元度的拟议方法的趋同率。一系列数字实验证实了我们的理论结果并探索了其他方面,例如重建的质量如何取决于所涉域的几何性。我们发现,某些凝固性特性对于在数据领域之外妥善恢复波流迁移至关重要,而更高的多元性定单可能更有效,但也更敏感于问题的不良性质。