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Surface energies and surface elasticity largely affect the mechanical response of nanostructures as well as the physical phenomenon associated with surfaces such as evaporation and adsorption. Studying surface energies at finite…

Materials Science · Physics 2022-07-18 Shashank Saxena , Miguel Spinola , Prateek Gupta , Dennis M. Kochmann

Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…

Numerical Analysis · Mathematics 2025-06-24 Robert C. Kirby , John D. Stephens

This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…

Numerical Analysis · Mathematics 2026-05-05 Ban Li , Bangmin Wu

We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.

Optics · Physics 2013-10-11 S. Burger , L. Zschiedrich , J. Pomplun , F. Schmidt

We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…

Numerical Analysis · Mathematics 2018-01-03 Peter Hansbo , Tobias Jonsson , Mats G. Larson , Karl Larsson

We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input…

A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless…

Numerical Analysis · Mathematics 2013-03-26 Maxim A. Olshanskii , Arnold Reusken , Xianmin Xu

We propose a numerical method for fluid deformable surfaces governed by surface Stokes flow and Helfrich bending energy under active growth, aiming to model shape evolution of the epithelium in developmental processes. To prevent…

Fluid Dynamics · Physics 2026-02-17 Maik Porrmann , Sören Bartels , Axel Voigt

The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…

Numerical Analysis · Mathematics 2019-03-19 Piotr Swierczynski , Barbara Wohlmuth

A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a…

Soft Condensed Matter · Physics 2022-02-02 Eduardo Vitral , Perry H. Leo , Jorge Viñals

We introduce an enriched immersed finite element method for addressing interface problems characterized by general non-homogeneous jump conditions. Unlike many existing unfitted mesh methods, our approach incorporates a homogenization…

Numerical Analysis · Mathematics 2025-05-07 Ruchi Guo , Xu Zhang

An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…

Numerical Analysis · Mathematics 2016-05-30 Xue Jiang , Peijun Li , Junliang Lv , Weiying Zheng

In the present work, the evolution of damage in periodic composite materials is investigated through a novel finite element-based multiscale computational approach. The methodology is developed by means of the original combination of…

Numerical Analysis · Mathematics 2019-08-09 Francesca Fantoni , Andrea Bacigalupo , Marco Paggi , Josè Reinoso

Surface energy is fundamental in controlling surface properties and surface-driven processes like heterogeneous catalysis, as adsorption energy is. It is thus crucial to establish an effective scheme to determine surface energy and its…

Materials Science · Physics 2020-09-22 Bo Li , Xin Li , Wang Gao , Qing Jiang

This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…

Numerical Analysis · Mathematics 2017-10-24 Yujie Liu , Junping Wang , Qingsong Zou

We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…

Numerical Analysis · Mathematics 2022-01-14 Anton Arnold , Sjoerd Geevers , Ilaria Perugia , Dmitry Ponomarev

In this paper we describe a new model for solidification with heat flux using the phase field crystal (PFC) framework. The equations are thermodynamically consistent, in the sense that the time rate of change of the entropy density is…

Materials Science · Physics 2021-07-13 C. Wang , S. M. Wise

The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g_1 and step-step interaction energy g_3>0. For diffusion-limited…

Materials Science · Physics 2009-11-10 Dionisios Margetis , Michael J. Aziz , Howard A. Stone

The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete…

Numerical Analysis · Mathematics 2023-10-16 Maxim A. Olshanskii , Arnold Reusken , Paul Schwering

Space group theory is pivotal in the design of nanophotonics devices, enabling the characterization of periodic optical structures such as photonic crystals. The aim of this study is to extend the application of nonsymmorphic space groups…

Optics · Physics 2025-06-02 Lida Liu , Jingwei Wang , Yuhao Jing , Songzi Lin , Zhongfei Xiong , Yuntian Chen