Related papers: On the finite element approximation for non-statio…
We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier--Stokes equations. The numerical solution on a convenient…
In this paper, we propose and analyze a fully discrete finite element projection method for the magnetohydrodynamic (MHD) equations. A modified Crank--Nicolson method and the Galerkin finite element method are used to discretize the model…
We study the steady state motion of incompressible and viscous fluid flow in a rotating reference frame where vortices may take place. An approximated analytic solution of the Stokes flow problem is proposed for situations where the…
The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves…
$L^2$ norm error estimates of semi- and full discretisations, using bulk--surface finite elements and Runge--Kutta methods, of wave equations with dynamic boundary conditions are studied. The analysis resides on an abstract formulation and…
In this paper, we consider a stationary, constant viscosity, incompressible Stokes flow with singular forces along one or several interfaces. Assuming only the jumps of the pressure are present along the interface, we develop a new…
The primary data which determine the evolution of glaciation are the bedrock elevation and the surface mass balance. From this data, which we assume is defined over a fixed land region, the glacier's geometry solves a free boundary problem…
We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…
Recently, the $P_1$-nonconforming finite element space over square meshes has been proved stable to solve Stokes equations with the piecewise constant space for velocity and pressure, respectively. In this paper, we will introduce its…
We consider nonstationary Stokes equations in nondivergence form with variable viscosity coefficients and generalized Navier slip boundary conditions with slip tensor $\mathcal{A}$ in a domain $\Omega$ in $\mathbb{R}^d$. First, under the…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
We present here a general method based on the investigation of the relative energy of the system, that provides an unconditional error estimate for the approximate solution of the barotropic Navier Stokes equations obtained by time and…
In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…
We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…
A low-order finite element method is constructed and analysed for an incompressible non-Newtonian flow problem with power-law rheology. The method is based on a continuous piecewise linear approximation of the velocity field and piecewise…
The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…