Unique continuation for the Helmholtz equation using stabilized finite element methods
Unique continuation for the Helmholtz equation using stabilized finite element methods
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DOI：
10.1016/j.matpur.2018.10.003
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发表时间：
2017-10
期刊：
影响因子：
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通讯作者：
E. Burman;Mihai Nechita;L. Oksanen
中科院分区：
文献类型：
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作者：
E. Burman;Mihai Nechita;L. Oksanen
在这项工作中，我们考虑了一个独特的连续性问题的亥姆霍兹方程使用稳定的有限元方法的计算近似。第一个条件稳定性估计，根据凸性假设的几何形状，常数增长最多线性波数。然后，这些估计被用来获得误差界的有限元方法是明确的波数。给出了一些数值例子。
In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity assumption on the geometry, the constants grow at most linearly in the wave number. Then these estimates are used to obtain error bounds for the finite element method that are explicit with respect to the wave number. Some numerical illustrations are given.