Related papers: Fractal homogenization of multiscale interface pro…
The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial…
The impact of inhomogeneous arrangement of nodes in space on network organization cannot be neglected in most of real-world scale-free networks. Here, we wish to suggest a model for a geographical network with nodes embedded in a fractal…
Elliptic homogenization is used to determine coarse-grained properties of materials with features on small scales for heat transfer and elasticity. When microstructural features of a material have rapid, periodic fluctuations, the solution…
We consider divergence form elliptic operators in dimension $n\geq 2$ with $L^\infty$ coefficients. Although solutions of these operators are only H\"{o}lder continuous, we show that they are differentiable ($C^{1,\alpha}$) with respect to…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
We study the homogenization for a class of non-symmetric pure jump Feller processes. The jump intensity involves periodic and aperiodic constituents, as well as oscillating and non-oscillating constituents. This means that the noise can…
We consider the homogenization of a semilinear elliptic equation where the coefficients of the second-order differential operator may be discontinuous. We establish the existence and uniqueness of the fine-scale solution, followed by an a…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation…
We develop a continuum limit and mean-field theory for interacting particle systems (IPS) on self-similar networks, a new class of discrete models whose large-scale behavior gives rise to nonlocal evolution equations on fractal domains.…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of…
Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the…
In this paper, we present and analyze an unfitted finite element method for the elliptic interface problem. We consider the case that the interface is $C^2$-smooth or polygonal, and the exact solution $u \in H^{1+s}(\Omega_0 \cup \Omega_1)$…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…
In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in $\mathbb{R}^2$ with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the…
Elliptic interface problems whose solutions are $C^0$ continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable generalized finite element method (SGFEM) and immersed FEM…
This paper analyses the problem of a semi-infinite fluid-driven fracture propagating through multiple stress layers in a permeable elastic medium. Such a problem represents the tip region of a planar hydraulic fracture. When the hydraulic…
The question is studied whether weak solutions of linear partial integrodifferential equations approach a constant spatial profile after rescaling, as time goes to infinity. The possible limits and corresponding scaling functions are…
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…