论文标题
通过不断发展的界面发展有限元素以进行对流扩散
Evolving finite elements for advection diffusion with an evolving interface
论文作者
论文摘要
本文的目的是开发一种数值方案，以基于抽象发展的有限元元素框架近似抛物线方程的界面问题（C M Elliott，T Ranner，Ima J Num Analy，41：3，2021，doi：10.1093/imanum/draaa062）。该问题的适当弱公式是用于使用旨在适应移动界面的不断发展的有限元素的。最佳订单误差范围被证明是针对不断发展的等级有限元素的。本文以模型问题验证收敛顺序的模型问题的数值结果结束。
The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3, 2021, doi:10.1093/imanum/draa062). An appropriate weak formulation of the problem is derived for the use of evolving finite elements designed to accommodate for a moving interface. Optimal order error bounds are proved for arbitrary order evolving isoparametric finite elements. The paper concludes with numerical results for a model problem verifying orders of convergence.
