Related papers: A finite element method for anisotropic crystal gr…
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…
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…
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,…
We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…