Related papers: Embedded corrector problems for homogenization in …
Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…
We consider the mathematical analysis and homogenization of a moving boundary problem posed for a highly heterogeneous, periodically perforated domain. More specifically, we are looking at a one-phase thermo-elasticity system with phase…
We propose a generalized finite element method for linear elasticity equations with highly varying and oscillating coefficients. The method is formulated in the framework of localized orthogonal decomposition techniques introduced by…
Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments. The paper considers a linear elasticity system with strongly heterogeneous coefficients and…
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these…
Motivated by recent interest in elastic problems in which the target space is non-Euclidean, we study a limit where local rest distances within an elastic body are incompatible, yet close to, distances within the ambient space.…
We formalize and study the natural approach of designing convex surrogate loss functions via embeddings, for problems such as classification, ranking, or structured prediction. In this approach, one embeds each of the finitely many…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
We consider a non-stationary Stokes-Nernst-Planck-Poisson system posed in perforated domains. Our aim is to justify rigorously the homogenization limit for the upscaled system derived by means of two-scale convergence in \cite{RMK12}. In…
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
In this paper a second-order homogenization approach for periodic material is derived from an appropriate representation of the down-scaling that correlates the microdisplacement field to the macro-displacement field and the macro-strain…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…
We use uniform $W^{2,p}$ estimates to obtain corrector results for periodic homogenization problems of the form $A(x/\varepsilon):D^2 u_{\varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition. We propose and rigorously…
We obtain an error estimate between viscosity solutions and \delta-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides uniform ellipticity, is that the nonlinearity is…
In this paper, we deal with the inverse problem of the shape reconstruction of cavities and inclusions embedded in a linear elastic isotropic medium from boundary displacement's measurements. For, we consider a constrained minimization…
Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…
The perfectly matched layer is very important for the elastic wave problem in the frequency domain. Generally, the formulas of the elasticity tensor in the perfectly matched layers are derived from the transformed momentum equation. In this…