有限元法
离散化
参数统计
分段
先验与后验
数学
背景(考古学)
应用数学
平面的
混合有限元法
扩展有限元法
参数方程
数学分析
数学优化
几何学
计算机科学
计算机图形学(图像)
物理
认识论
哲学
统计
古生物学
热力学
生物
作者
Christoph Lehrenfeld,Arnold Reusken
出处
期刊:Ima Journal of Numerical Analysis
日期:2017-08-18
卷期号:38 (3): 1351-1387
被引量:44
标识
DOI:10.1093/imanum/drx041
摘要
In the context of unfitted finite element discretizations, the realization of high-order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method that achieves a high-order approximation of the geometry for domains that are implicitly described by smooth-level set functions. The method is based on a parametric mapping, which transforms a piecewise planar interface reconstruction to a high-order approximation. Both components, the piecewise planar interface reconstruction and the parametric mapping, are easy to implement. In this article, we present an a priori error analysis of the method applied to an interface problem. The analysis reveals optimal order error bounds for the geometry approximation and for the finite element approximation, for arbitrary high-order discretization. The theoretical results are confirmed in numerical experiments.
科研通智能强力驱动
Strongly Powered by AbleSci AI