Related papers: Optimal higher derivative estimates for Stokes equ…
In this paper, we establish higher-order derivative estimates for the Stokes equations in a three-dimensional domain containing two closely spaced rigid inclusions. We construct a sequence of auxiliary functions via an inductive process to…
In this paper, we establish the estimates for the gradient and the second-order partial derivatives for the Stokes flow in the presence of two closely located strictly convex inclusions in dimension three. Moreover, the blow-up rate of the…
It is vital important in material sciences and fluid mechanics to study the field enhancements in the narrow region between two inclusions. Complex fluids including particle suspensions usually result in complicated flow behavior. In this…
The stress concentration is a common phenomenon in the study of fluid-solid model. In this paper, we investigate the boundary gradient estimates and the second order derivatives estimates for the Stokes flow when the rigid particles…
When two inclusions with high contrast material properties are located close to each other in a homogeneous medium, stress may become arbitrarily large in the narrow region between them. In this paper, we investigate such stress…
We investigate higher derivative estimates for the Lam\'e system with hard inclusions embedded in a bounded domain in $\mathbb{R}^{d}$. As the distance $\varepsilon$ between two closely spaced hard inclusions approaches zero, the stress in…
In this paper we investigate the stress concentration problem that occurs when two convex rigid particles are closely immersed in a fluid flow. The governing equations for the fluid flow are the stationary incompressible Navier-Stokes…
In this paper, a mathematical model of two adjacent rigid particles immersed into a viscous incompressible fluid is considered. The main feature of the flow is that the Cauchy stress tensor consisting of the strain tensor and the pressure…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
An enriched hybrid high-order method is designed for the Stokes equations of fluid flow and is fully applicable to generic curved meshes. Minimal regularity requirements of the enrichment spaces are given, and an abstract error analysis of…
In the region between two closely located stiff inclusions, the stress, which is the gradient of a solution to the Lam\'{e} system with partially infinite coefficients, may become arbitrarily large as the distance between interfacial…
We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…
We present an efficient, accurate, and robust method for simulation of dense suspensions of deformable and rigid particles immersed in Stokesian fluid in two dimensions. We use a well-established boundary integral formulation for the…
The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…
It is an interesting and important topic to study the motion of small particles in a viscous liquid in current applied research. In this paper we assume the particles are convex with arbitrary shapes and mainly investigate the interaction…
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…
Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes-Darcy model with Beaver-Joseph-Saffman interface condition in literatures, the numerical analysis only get…
The three-dimensional jump conditions for the pressure and velocity fields, up to the second normal derivative,across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise…
We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium. The governing equation may be degenerate of $p-$Laplace type, with $1<p \leq N$. We…
This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…