表面四阶界面问题的混合沉浸式有限元法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2024-09-24 DOI:10.1016/j.camwa.2024.09.012

Jiaqi Chen, Xufeng Xiao, Xinlong Feng

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引用次数: 0

摘要

本文首次尝试对表面的四阶界面问题进行数值计算。本文提出了一种基于 Ciarlet-Raviart 公式的混合沉浸表面有限元方法，用于求解具有三种边界条件的问题。这种方法的一个重要优点是可以避免生成复杂的体拟合表面网格。根据混合公式给出了沉入式表面有限元空间。通过修改数值解的表示方法，该方法被扩展用于解决具有非均质通量跳跃条件的四阶界面问题。给出的数值示例说明了所提方法的能力。

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A mixed immersed finite element method for fourth-order interface problems on surfaces

This paper presents the first numerical attempt on fourth-order interface problems on surfaces. A mixed immersed surface finite element method based on Ciarlet-Raviart formulation is proposed for solving the problem with three types of boundary conditions. One important advantage of this method is that it can avoid the generation of complex body-fitting surface meshes. The immersed surface finite element space is given based on the mixed formulation. By modifying the representation of numerical solutions, the method is extended to solve the fourth-order interface problem with nonhomogeneous flux jump conditions. Numerical examples are given to illustrate the capabilities of the proposed method.

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来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).