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This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…

Numerical Analysis · Mathematics 2022-09-02 Shuhao Cao , Long Chen , Ruchi Guo , Frank Lin

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…

Numerical Analysis · Mathematics 2017-06-27 Christoph Lehrenfeld , Arnold Reusken

Maxwell interface problems are of great importance in many electromagnetic applications. Unfitted mesh methods are especially attractive in 3D computation as they can circumvent generating complex 3D interface-fitted meshes. However, many…

Numerical Analysis · Mathematics 2022-05-30 Long Chen , Ruchi Guo , Jun Zou

An $hp$ version of interface penalty finite element method ($hp$-IPFEM) is proposed for elliptic interface problems in two and three dimensions on unfitted meshes. Error estimates in broken $H^1$ norm, which are optimal with respect to $h$…

Numerical Analysis · Mathematics 2010-07-20 Haijun Wu , Yuanming Xiao

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

Numerical Analysis · Mathematics 2026-03-27 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…

Numerical Analysis · Mathematics 2018-08-29 Natalie N. Beams , Andreas Klöckner , Luke N. Olson

In this paper, we develop geometry-conforming immersed finite element (IFE) spaces on triangular meshes for elliptic interface problems. The construction is built on a Frenet-Serret mapping that transforms a smooth interface curve into a…

Numerical Analysis · Mathematics 2026-05-25 Yuanhui Lin , Xu Zhang , Tao Lin

In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite…

Numerical Analysis · Mathematics 2017-02-16 Waixiang Cao , Xu Zhang , Zhimin Zhang

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…

Numerical Analysis · Mathematics 2017-09-01 Christoph Lehrenfeld , Arnold Reusken

In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points. We construct new IFE functions on elements intersected with…

Numerical Analysis · Mathematics 2020-03-04 Yuan Chen , Songming Hou , Xu Zhang

In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…

Numerical Analysis · Mathematics 2019-10-18 Cuiyu He , Xu Zhang

A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated Q1 nonconforming finite elements with the integral-value…

Numerical Analysis · Mathematics 2019-10-18 Tao Lin , Dongwoo Sheen , Xu Zhang

This paper presents a mini immersed finite element (IFE) method for solving two- and three-dimensional two-phase Stokes problems on Cartesian meshes. The IFE space is constructed from the conventional mini element, with shape functions…

Numerical Analysis · Mathematics 2024-09-02 Haifeng Ji , Dong Liang , Qian Zhang

In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…

Numerical Analysis · Mathematics 2025-09-17 Lin Yang , Qilong Zhai

In this article, we develop and analyze a finite element method with the first family N\'ed\'elec elements of the lowest degree for solving a Maxwell interface problem modeled by a $\mathbf{H}(\text{curl})$-elliptic equation on unfitted…

Numerical Analysis · Mathematics 2020-11-25 Ruchi Guo , Yanping Lin , Jun Zou

Artificial Intelligence (AI)-driven defect inspection is pivotal in industrial manufacturing. Yet, many methods, tailored to specific pipelines, grapple with diverse product portfolios and evolving processes. Addressing this, we present the…

Computer Vision and Pattern Recognition · Computer Science 2024-09-24 Jiaqi Tang , Hao Lu , Xiaogang Xu , Ruizheng Wu , Sixing Hu , Tong Zhang , Tsz Wa Cheng , Ming Ge , Ying-Cong Chen , Fugee Tsung

In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…

Computational Physics · Physics 2026-02-18 F. Şık , F. L. Teixeira , B. Shanker

In this paper, we present and analyze an unfitted finite element method for the elliptic interface problem. We consider the case that the interface is $C^2$-smooth or polygonal, and the exact solution $u \in H^{1+s}(\Omega_0 \cup \Omega_1)$…

Numerical Analysis · Mathematics 2026-01-12 Fanyi Yang

We consider the approximation of eigenvalue problems for elasticity equations with interface. This kind of problems can be efficiently discretized by using immersed finite element method (IFEM) based on Crouzeix-Raviart P1-nonconforming…

Numerical Analysis · Mathematics 2015-06-04 Seungwoo Lee , Do Y. Kwak , Imbo Sim

Video frame interpolation~(VFI) algorithms have improved considerably in recent years due to unprecedented progress in both data-driven algorithms and their implementations. Recent research has introduced advanced motion estimation or novel…

Computer Vision and Pattern Recognition · Computer Science 2022-07-26 Zhixiang Chi , Rasoul Mohammadi Nasiri , Zheng Liu , Yuanhao Yu , Juwei Lu , Jin Tang , Konstantinos N Plataniotis