In this work, we illustrate the connection between adaptive mesh refinement for finite element discretized PDEs and the recently developed \emph{bi-level regularization algorithm}. By adaptive mesh refinement according to data noise, regularization effect and convergence are immediate consequences. We moreover demonstrate its numerical advantages to the classical Landweber algorithm in term of time and reconstruction quality for the example of the Helmholtz equation in an aeroacoustic setting.

翻译：本文阐述了有限元离散偏微分方程的自适应网格细化与近期提出的\emph{双层正则化算法}之间的关联。通过根据数据噪声进行自适应网格细化，正则化效应与收敛性得以直接实现。此外，以气动声学环境中的亥姆霍兹方程为例，我们证明了该方法在计算时间与重建质量方面相较于经典的Landweber算法具有数值优势。