Related papers: Error Estimates of Reiterated Stokes Systems via F…
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…
We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an…
Understanding the flow of complex media is relevant for a wide range of research fields and industrial applications. Several numerical approaches exist by which approximate solutions can be determined for the Stokes equations that describe…
This paper studies the convergence rates in $L^2$ and $H^1$ of Dirichelt problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.
We design and analyze a posteriori error estimators for the Stokes system with singular sources in suitable $\mathbf{W}^{1,p}\times \mathrm{L}^p$ spaces. We consider classical low-order inf-sup stable and stabilized finite element…
In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…
For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handling the divergence-free condition of the Stokes equation is…
In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on analysis of oscillatory integrals. In the uniformly convex…
We consider the homogenization of the Stokes equations in a domain perforated with a large number of small holes which are periodically distributed. In [1,2], Allaire gave a systematic study on this problem. In this paper, we introduce a…
This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…
In this work we propose and study a three field mixed formulation for solving the Stokes problem with Tresca-type non-linear boundary conditions. Two Lagrange multipliers are used to enforce div(u)=0 constraint and to regularize the energy…
The two dimensional Navier-Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic…
We consider the homogenisation of the Stokes equations in a porous medium which is evolving in time. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables to model a…
We generalize pressure boundary conditions of an $\varepsilon$-Stokes problem. Our $\varepsilon$-Stokes problem connects the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter $\varepsilon>0$. For…
In our recent work [8], we have studied the homogenization of the Poisson equation in a class of non periodically perforated domains. In this paper, we examine the case of the Stokes system. We consider a porous medium in which the…
For a family of stabilized mixed finite element methods for the Stokes equations a complete a priori and a posteriori error analysis is given.
We consider the homogenization of the compressible Navier-Stokes-Fourier equations in a randomly perforated domain in $\mathbb{R}^3$. Assuming that the particle size scales like $\varepsilon^\alpha$, where $\varepsilon>0$ is their mutual…
This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely, we establish a large-scale regularity theory for this…
The time-periodic Stokes problem in a half-space with fully inhomogeneous right-hand side is investigated. Maximal regularity in a time-periodic Lp setting is established. A method based on Fourier multipliers is employed that leads to a…
We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…