Related papers: Divergence-free tangential finite element methods …
The paper develops and analyzes a higher-order unfitted finite element method for the incompressible Stokes equations, which yields a strongly divergence-free velocity field up to the physical boundary. The method combines an isoparametric…
We develop the analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are…
In this paper, we construct and analyze divergence-free finite element methods for the Stokes problem on smooth domains. The discrete spaces are based on the Scott-Vogelius finite element pair of arbitrary polynomial degree greater than…
We present a class of Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for the incompressible flow with moving boundaries and interfaces including two-phase flow with surface tension.
We present a new method for approximating solutions to the incompressible miscible displacement problem in porous media. At the discrete level, the coupled nonlinear system has been split into two linear systems that are solved…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
Solving the Navier-Stokes equations when the density field contains a large sharp discontinuity---such as a water/air free surface---is numerically challenging. Convective instabilities cause Gibbs oscillations which quickly destroy the…
In this note we design a cut finite element method for a low order divergence free element applied to a boundary value problem subject to Stokes' equations. For the imposition of Dirichlet boundary conditions we consider either Nitsche's…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
This paper proposes and analyzes a class of weak Galerkin (WG) finite element methods for stationary natural convection problems in two and three dimensions. We use piecewise polynomials of degrees k, k-1, and k(k>=1) for the velocity,…
Within the last years pressure robust methods for the discretization of incompressible fluids have been developed. These methods allow the use of standard finite elements for the solution of the problem while simultaneously removing a…
We establish a simple, rigorous, and easy to implement connection between the classical continuous finite element method (FEM) and the discontinuous Galerkin (DG) method for Poisson's problem. The key idea is to insert a vanishing-thickness…
A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…
The Stokes equation posed on surfaces is important in some physical models, but its numerical solution poses several challenges not encountered in the corresponding Euclidean setting. These include the fact that the velocity vector should…
The accurate numerical simulation of high Reynolds number incompressible flows is a challenging topic in computational fluid dynamics. Classical inf-sup stable methods like the Taylor-Hood element or only $L^2$-conforming discontinuous…
Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the…
A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method,…
This paper is concerned with finite element approximations of $W^{2,p}$ strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients. A nonstandard (primal)…
In this paper, we consider multipoint flux mixed finite element discretizations for slightly compressible Darcy flow in porous media. The methods are formulated on general meshes composed of triangles, quadrilaterals, tetrahedra or…
This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution…