Related papers: A stabilized Nitsche fictitious domain method for …
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the…
The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with…
This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the motion of an incompressible homogeneous fluid in a bounded 2D or…
In this paper we consider stabilised finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three…
A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal…
In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity $\nu$ in an axis-aligned domain $\Omega$. We decouple the velocity $\bm u$ and pressure $p$ by deriving a novel biharmonic…
This article is concerned with the discretisation of the Stokes equations on time-dependent domains in an Eulerian coordinate framework. Our work can be seen as an extension of a recent paper by Lehrenfeld & Olshanskii [ESAIM: M2AN,…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
We implement a stabilized finite element method for steady Darcy-Brinkman-Forchheimer model within the continuous Galerkin framework. The nonlinear fluid model is first linearized using a standard \textit{Newton's method. The sequence of…
In this paper we propose, analyze, and test numerically a pressure-robust stabilized finite element for a linearized problem in incompressible fluid mechanics, namely, the steady Oseen equation with low viscosity. Stabilization terms are…
In this article we obtain an optimal best approximation type result for fully discrete approximations of the transient Stokes problem. For the time discretization we use the discontinuous Galerkin method and for the spatial discretization…
Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the…
We propose and analyze a finite element method for a semi-stationary Stokes system modeling compressible fluid flow subject to a Navier-slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element…
We present guidelines for deriving new Nitsche Finite Element Methods to enforce equality and inequality constraints that act on the value of the unknown mechanical quantity. We first formulate the problem as a stabilized finite element…
Solving the Stokes equation by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions whose discretisation is not trivial. For this reason the use of approximation methods such as…
We provide an error analysis for the solution of the nonstationary Stokes problem by a variational method in space and time. We use finite elements of higher order for the approximation in space and a Galerkin-Petrov method with first order…
In this paper we establish best approximation type error estimates for the fully discrete Galerkin solutions of the time-dependent Stokes problem using the stream-function formulation. For the time discretization we use the discontinuous…
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…
It is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf-sup approximation stability even if a stable high fidelity method was used to generate…
We introduce an unfitted Nitsche finite element method with a new ghost-penalty stabilization based on local projection of the solution gradient. The proposed ghost-penalty operator is straightforward to implement, ensures algebraic…