论文标题
解决有限元素的三维界面问题：A-Priori误差分析
Solving Three-Dimensional Interface Problems with Immersed Finite Elements: A-Priori Error Analysis
论文作者
论文摘要
在本文中，我们开发和分析了一种三维的有限元方法，用于解决三维椭圆界面问题。所提出的方法可以用于界面未配置的网格，例如由长方体组成的笛卡尔网格。我们为具有任意接口切割配置的接口元素建立了三联IFE功能的迹线和逆不等式。最佳的先验误差估计在能量和L2规范中均得到严格证明。提供数值示例不仅是为了验证我们的理论结果，而且还证明了这种IFE方法在处理一些现实世界3D接口模型时的适用性。
In this paper, we develop and analyze a trilinear immersed finite element method for solving three-dimensional elliptic interface problems. The proposed method can be utilized on interface-unfitted meshes such as Cartesian grids consisting of cuboids. We establish the trace and inverse inequalities for trilinear IFE functions for interface elements with arbitrary interface-cutting configuration. Optimal a priori error estimates are rigorously proved in both energy and L2 norms. Numerical examples are provided not only to verify our theoretical results but also to demonstrate the applicability of this IFE method in tackling some real-world 3D interface models.
