In this paper, we consider the initial-boundary value problem for the three-dimensional
incompressible magnetohydrodynamic equations. We first establish certain regularity results …

A fully discrete two-level finite element method (the two-level method) is presented for
solving the two-dimensional time-dependent Navier--Stokes problem. The method requires …

This paper considers three iterative methods for solving the stationary Navier–Stokes
equations. Iterative method I consists in solving the stationary Stokes equations, iterative …

In this paper, we study the stability and convergence of the Crank–Nicolson/Adams–
Bashforth scheme for the two-dimensional nonstationary Navier–Stokes equations. A finite …

This paper considers the stability and convergence results for the Euler implicit/explicit
scheme applied to the spatially discretized two-dimensional (2D) time-dependent Navier …

This paper is concerned with the development and analysis of a new stabilized finite
element method based on two local Gauss integrations for the two-dimensional transient …

We propose and study two second-order in time implicit-explicit methods for the coupled
Stokes--Darcy system that governs flows in karst aquifers and other subsurface flow …

Recently, engineers, scientists, and mathematicians have concentrated their efforts on
numerical methods for solving the Navier–Stokes equations. The reason is that these …

This paper considers the long-time stability property of a popular semi-implicit scheme for
the two-dimensional incompressible Navier–Stokes equations in a periodic box that treats …

The unconditional stability and convergence analysis of the Euler implicit/explicit scheme
with finite element discretization are studied for the incompressible time-dependent Navier …