Related papers: A cut finite element method for a Stokes interface…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
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…
Having a finite interfacial thickness, the phase-field models supply a way to model the fluid interfaces, which allows the calculations of the interface movements and deformations on the fixed grids. Such modeling is applied to the…
We define a finite element method for the coupling of Stokes and nonlinear Poisson--Boltzmann equations. The novelty in the formulation is that the coupling from the electric potential to the drag in the momentum balance is rewritten as a…
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…
This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite element (FE) spaces for each component of the velocity field are considered. We consider some new combinations of…
We consider two-level finite element discretization methods for the stream function formulation of the Navier-Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh, then solving a linear…
The aim of this paper is to propose a systematic way to obtain convergent finite element schemes for the Darcy-Stokes flow problem by combining well-known mixed finite elements that are separately convergent for Darcy and Stokes problems.…
In this paper, we combine the multiscale flnite element method to propose an algorithm for solving the non-stationary Stokes-Darcy model, where the permeability coefflcient in the Darcy region exhibits multiscale characteristics. Our…
This paper provides mathematical analysis of an elementary fully discrete finite difference method applied to inhomogeneous (non-constant density and viscosity) incompressible Navier-Stokes system on a bounded domain. The proposed method…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…
We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport…
We propose and analyse an augmented mixed finite element method for the Navier--Stokes equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and no-slip boundary conditions. The weak formulation…
In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…
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…
We study the Stokes--Poisson--Boltzmann equations with Dirichlet and Navier boundary conditions. The system consists of the incompressible Stokes equations coupled with a nonlinear Poisson--Boltzmann equation through electrostatic forcing…
Stability and error analysis of a hybridized discontinuous Galerkin finite element method for Stokes equations is presented. The method is locally conservative, and for particular choices of spaces the velocity field is point-wise…