SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A859-A882, January 2021.
We design and analyze a Hybrid High-Order (HHO) method on unfitted meshes to approximate elliptic interface problems by means of a consistent penalty method à la Nitsche. The curved interface can cut through the mesh cells in a rather general fashion. Robustness with respect to the cuts is achieved by using a cell agglomeration technique, and robustness with respect to the contrast in the diffusion coefficients is achieved by using a different gradient reconstruction on each side of the interface. A key novel feature of the gradient reconstruction is to incorporate a jump term across the interface, thereby releasing the Nitsche penalty parameter from the constraint of being large enough. Error estimates with optimal convergence rates are established. A robust cell agglomeration procedure limiting the agglomerations to the nearest neighbors is devised. Numerical simulations for various interface shapes corroborate the theoretical results.

中文翻译：

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椭圆界面问题的不适合的混合高阶单元集混合高阶方法

SIAM科学计算杂志，第43卷，第2期，第A859-A882页，2021年1月。
我们设计并分析了一种非拟合网格上的混合高阶（HHO）方法，通过一种一致的罚分方法àla Nitsche来近似椭圆界面问题。弯曲的界面可以以相当普通的方式切穿网孔。通过使用单元聚集技术，可以实现对切口的鲁棒性，并且通过在界面的每一侧使用不同的梯度重建，可以实现相对于扩散系数的对比度的鲁棒性。梯度重建的一个关键的新颖特征是在界面上合并一个跳跃项，从而从足够大的约束中释放了Nitsche罚分参数。建立具有最佳收敛速度的误差估计。设计了一种鲁棒的单元集聚程序，将集聚限制到最近的邻居。各种界面形状的数值模拟证实了理论结果。