Solving Three-Dimensional Interface Problems with Immersed Finite Elements: A-Priori Error Analysis

DOI10.1016/J.JCP.2021.110445arXiv2004.08984WikidataQ114163447 ScholiaQ114163447MaRDI QIDQ6339010

Publication date: 19 April 2020

Abstract: 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.

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)

This page was built for publication: Solving Three-Dimensional Interface Problems with Immersed Finite Elements: A-Priori Error Analysis

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6339010)