论文标题
自动网格生成的椭圆界面问题的任意高阶未有限元方法
An Arbitrarily High Order Unfitted Finite Element Method for Elliptic Interface Problems with Automatic Mesh Generation
论文作者
论文摘要
我们考虑在载有椭圆界面问题的悬挂节点上的高阶未有限元方法的可靠实现。我们构建了一种可靠的算法，以将小界面元素与周围元素合并，以自动生成有限元网格，其元素相对于两个域而言是较大的。我们为界面元素提出了新的基础函数，以根据有限元近似顺序，网格元素数量以及量化界面几何形状的网格分辨率的界面偏差来控制刚度矩阵的条件数量的生长。提出了数值示例，以说明该方法的竞争性能。
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.
