论文标题
一种丰富的沉浸式有限元方法，用于与非均匀跳跃条件的接口问题
An Enriched Immersed Finite Element Method for Interface Problems with Nonhomogeneous Jump Conditions
论文作者
论文摘要
本文介绍并分析了$ p^{th} $ - 浸入有限元素（IFE）方法，用于椭圆接口问题，具有非均匀跳跃条件的问题。在这种方法中，通过基本的IFE和IFE IFE分段多项式函数来最佳地近似跳跃条件，该功能通过在接口元素上求解局部Cauchy问题构建。所提出的IFE方法基于接口元素上的不连续的Galerkin公式和非接口元素上的连续Galerkin公式。证明此$ p^{th} $ - ife方法可以在网状细化下最佳收敛。此外，本文解决了此IFE方法的稳定性，并为其条件数建立了上限，这些数字相对于网格尺寸是最佳的，但相对于不连续系数的对比度而言是次优的。
This article presents and analyzes a $p^{th}$-degree immersed finite element (IFE) method for elliptic interface problems with nonhomogeneous jump conditions. In this method, jump conditions are approximated optimally by basic IFE and enrichment IFE piecewise polynomial functions constructed by solving local Cauchy problems on interface elements. The proposed IFE method is based on a discontinuous Galerkin formulation on interface elements and a continuous Galerkin formulation on non-interface elements. This $p^{th}$-degree IFE method is proved to converge optimally under mesh refinement. In addition, this article addresses the stability of this IFE method and has established upper bounds for its condition numbers which are optimal with respect to the mesh size but suboptimal with respect to the contrast of the discontinuous coefficient.
