An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation

Abstract

In this talk, 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.

Speaker

刘勇，中科院数学与系统科学研究院，计算数学所，优秀青年副研究员。分别于2015年，2020年获中国科学技术大学学士和博士学位。2018年至2020年在美国布朗大学应用数学系联合培养。2020年至2022年在中科院数学与系统科学研究院，华罗庚数学科学中心做博士后。主要研究领域为高精度数值计算方法，包括间断有限元方法的算法设计及其数值分析、磁流体力学方程的数值模拟、非拟合网格有限元方法等。曾获2020年中科院院长奖特别奖，2021年中科院优博。2023年，获国家自然科学基金青年项目，入选中科院青年创新促进会，入选中科院数学与系统科学研究院“陈景润未来之星”人才计划。在SINUM, SISC, JCP等SCI期刊发表论文10余篇。