Related papers: An anisotropic mesh adaptation method for the fini…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…
We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type finite elements. The resulting discretizations are continuous in space, and continuous or discontinuous in time. In a…
We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule…
In this paper, we discuss the accuracy and the robustness of the mixed Virtual Element Methods when dealing with highly-anisotropic diffusion problems. In particular, we analyze the performances of different approaches which are…
In many astrophysical plasmas, the Coulomb collision is insufficient to maintain an isotropic temperature, and the system is driven to the anisotropic regime. In this case, magnetohydrodynamic (MHD) models with anisotropic pressure are…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
In this paper, we study the equilibria of an anisotropic, nonlocal aggregation equation with nonlinear diffusion which does not possess a gradient flow structure. Here, the anisotropy is induced by an underlying tensor field. Anisotropic…
Numerical modeling of elastic wave propagation in the subsurface requires applicability to heterogeneous, anisotropic and discontinuous media, as well as support of free surface boundary conditions. Here we study the cell-centered finite…
Grain growth in polycrystals is one of the principal mechanisms that take place during heat treatment of metallic components. This work treats an aspect of the anisotropic grain growth problem. By applying the first principles of…
We introduce a contact law for the normal force generated between two contacting, elastically anisotropic bodies of arbitrary geometry. The only requirement is that their surfaces be smooth and frictionless. This anisotropic contact law is…
The conventional Perfectly Matched Layer (PML) is unstable for certain kinds of anisotropic media. This instability is intrinsic and independent of PML formulation or implementation. The Multi-axial PML (MPML) removes such instability using…
A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equations. In the proposed method, the exterior domain…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
This paper is devoted to the multigrid convergence analysis for the linear systems arising from the conforming linear finite element discretization of the second order elliptic equations with anisotropic diffusion. The multigrid convergence…
In [Kopteva, Math. Comp., 2014] a counterexample of an anisotropic triangulation was given on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is…
We present a discretization for Darcy's problem using the recently developed Mimetic Spectral Element Method. The gist lies in the exact discrete representation of integral relations. In this paper, an anisotropic flow through a porous…
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,…
The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic…
We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence…