Solving three-dimensional interface problems with immersed finite elements: A-priori error analysis

[摘要] Immersed finite element methods are designed to solve interface problems on interface-unfitted meshes. However, most of the study, especially analysis, is mainly limited to the two-dimension case. In this paper, we provide an a priori analysis for the trilinear immersed finite element method to solve three-dimensional elliptic interface problems on 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 L-2 norms, with the constant in the error bound independent of the interface location and its dependence on coefficient contrast explicitly specified. 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. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-09-15

[关键词] Three-dimensional interface problem;Unfitted mesh method;Immersed finite element;Optimal error estimation