We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their surrounding elements to automatically generate the finite element mesh whose elements are large with respect to both domains. We propose new basis functions for the interface elements to control the growth of the condition number of the stiffness matrix in terms of the finite element approximation order, the number of elements of the mesh, and the interface deviation which quantifies the mesh resolution of the geometry of the interface. Numerical examples are presented to illustrate the competitive performance of the method.

翻译：我们考虑在卡尔提斯海绵上可靠地采用高阶不合格的限定元素方法,并挂接点解决椭圆界面问题。我们构建了可靠的算法,将小界面元素与周围元素合并,以自动生成在两个领域都有大量元素的有限元素网格。我们提议了界面元素的新基础功能,以控制硬度矩阵条件数的增长,即有限元素近似顺序、网状元素数量以及界面偏差,以测量界面几何学的网格分辨率。我们提供了数字实例,以说明该方法的竞争性性能。