相关论文: Eshelby-based homogenization schemes with finite c…
A multi-scale characterization of the field concentrations inside composite and polycrystalline media is developed. The analysis focuses on gradient fields associated with the intensive quantities given by the temperature and the electric…
We study uniform Lipschitz regularity estimates for elliptic systems in divergence form with continuous coefficients, based on rapidly oscillating periodic coefficients derived from homogenization theory. We extend a result by Avellaneda…
A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational…
We derive in this note a high-order corrector estimate for the homogenization of a microscopic semi-linear elliptic system posed in perforated domains. The major challenges are the presence of nonlinear volume and surface reaction rates.…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates…
A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…
The ratio between the couplings of a relaxational process to compression and shear, respectively, is calculated in the Eshelby picture of structural rearrangements within a surrounding elastic matrix, assuming a constant density of stable…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
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…
We describe the numerical scheme for the discretization and solution of 2D elliptic equations with strongly varying piecewise constant coefficients arising in the stochastic homogenization of multiscale composite materials. An efficient…
We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional…
We study the quantitative homogenization of linear second order elliptic equations in non-divergence form with highly oscillating periodic diffusion coefficients and with large drifts, in the so-called ``centered'' setting where…
In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…
Ellipsoidal harmonics are a useful generalization of spherical harmonics but present additional numerical challenges. One such challenge is in computing ellipsoidal normalization constants which require approximating a singular integral. In…
This paper investigates the singularities at the vertex of multiply connected angular inhomogeneities for heat conduction and elastic deformation. With the aid of Eshelby's equivalent inclusion method (EIM), each inhomogeneity is simulated…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…
We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…
This contribution is the numerically oriented companion article of the work [E. Canc\`es, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv preprint 1807.05131]. We focus here on the numerical resolution of the embedded corrector…