Related papers: A multiscale method for linear elasticity reducing…
We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the method, drastically reducing computation time. Here we show…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
This paper is to prove superconvergence of a family of simple conforming mixed finite elements of first orderfor the linear elasticity problem with the Hellinger--Reissner variational formulation. The analysis is based on three main…
We analyze the finite-strain Poynting-Thomson viscoelastic model. In its linearized small-deformation limit, this corresponds to the serial connection of an elastic spring and a Kelvin-Voigt viscoelastic element. In the finite-strain case,…
In this paper we present a new H(div)-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is…
We introduce the multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficient $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\boldsymbol{y}) =…
We establish interior Lipschitz estimates at the macroscopic scale for solutions to systems of linear elasticity with rapidly oscillating periodic coefficients and mixed boundary conditions in domains periodically perforated at a…
The operator-asymptotic approach was introduced by Lim-\v{Z}ubrini\'c in [Asymptotic Analysis. 141(4), p. 211-256 (2025)] for the homogenization of an $\varepsilon\mathbb{Z}^d$-periodic composite media. In this article, we consider the…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…
In this paper, a discontinuous Galerkin finite element method of Nitsche's version for the Steklov eigenvalue problem in linear elasticity is presented. The a priori error estimates are analyzed under a low regularity condition, and the…
This paper is an extension of the result by Christowiak and Kreisbeck (2017), which addresses the Gamma-convergence approach to a homogenization problem for composite materials consisting of two distinct types of parallel layers. In…
We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a…
We discuss the determination of the Lam\'e parameters of an elastic material by the means of boundary measurements. We will combine previous results of Eskin-Ralston and Isakov to prove inverse results in the case of bounded domains with…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
This article is concerned with uniform $C^{1,\alpha}$ and $C^{1,1}$ estimates in periodic homogenization of fully nonlinear elliptic equations. The analysis is based on the compactness method, which involves linearization of the operator at…
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement…
For a class of linear elliptic equations of general type with rapidly oscillating coefficients, we use the sigma-convergence method to prove the homogenization result and a corrector-type result. In the case of asymptotic periodic…
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such…
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of…