Related papers: A finite element method for anisotropic crystal gr…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
We present a numerical method to model the dynamics of inextensible biomembranes in a quasi-Newtonian incompressible flow, which better describes hemorheology in the small vasculature. We consider a level set model for the fluid-membrane…
In this paper, we have formulated a phase-field model based on the grand-potential functional for the simulation of precipitate growth in the presence of coherency stresses. In particular, we study the development of dendrite-like patterns…
ESFEM is a method introduced in order to solve a linear advection-diffusion equation on an evolving two-dimensional surface with finite elements by using a moving grid with nodes sitting on and evolving with the surface. The evolution of…
We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where…
In this work, we consider the solid-state dewetting of an axisymmetric thin film on a curved-surface substrate, with the assumption that the substrate morphology is also axisymmetric. Under the assumptions of axisymmetry, the surface…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
Porous materials are ubiquitous in various engineering and geological applications, where their permeability plays a critical role in viscous fluid flow and transport phenomena. Understanding and characterizing the microscale properties,…
We propose and study quantitative measures of smoothness which are adapted to anisotropic features such as edges in images or shocks in PDE's. These quantities govern the rate of approximation by adaptive finite elements, when no constraint…
Labourie raised the question of determining the possible asymptotics for the growth rate of compact $k$-surfaces, counted according to energy, in negatively curved $3$-manifolds, indicating the possibility of a theory of thermodynamical…
We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…
We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…
Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasi-continuum method links atomistic and…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…
This work presents an open-source interface that couples the viscoplastic self-consistent (VPSC) model capable of simulating anisotropic creep and irradiation growth in polycrystalline materials with the finite element solver Code_Aster.…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic…