In this paper, we consider the stability and convergence of fully discrete stabilized finite volume method for unsteady incompressible magnetohydrodynamics (MHD) equations on quasi-uniform regular triangulations. The spatial discretization is based lowest equal-order mixed element pair velocity, pressure magnetic fields, while time backward Euler semi-implicit scheme. order to overcome restrict...

In this paper we study the time dependent Stokes problem with mixed boundary conditions. The problem is discretized by the backward Euler’s scheme in time and finite elements in space. We establish an optimal a posteriori error with two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization.

The initial-boundary value problem for a linear parabolic equation with the Dirichlet boundary condition is solved approximately by applying the finite element discretization in the space dimension and three types of finite-difference discretizations in time: the backward, the Crank-Nicolson and the Calahan discretization. New error bounds are derived.

We analyze the discretization of the periodic initial value problem for Kuramoto–Sivashinsky type equations with Burgers nonlinearity by implicit– explicit backward difference formula (BDF) methods, establish stability and derive optimal order error estimates. We also study discretization in space by spectral methods.

The semi-implicit Euler discretization method is studied for abstract evolution equations in a Hilbert space H, like _ u = f(t; u; u) ; t 2 (0; T ] ; u(0) = u0, where f(t; ; v) is one-sided Lipschitz and R(I hf(t; ; v)) = H for h > 0 su ciently small, and f(t; u; ) is Lipschitz-continuous. Extension to Banach spaces is then pointed out. Ordinary and partial , di erential and integro-di erential...

In this work we study a preconditioned iterative method for some higher–order time discretizations of linear parabolic partial differential equations. We use the Padé approximations of the exponential function to discretize in time and show that standard solution algorithms for lower–order time discretization schemes, such as Crank–Nicolson and implicit Euler, can be reused as preconditioners f...

This work focuses on the extension of the recently introduced Spectral Difference Method to viscous flow. The spectral difference method is a conservative pseudo-spectral scheme based on a local collocation on unstructured elements. Recently results for scalar transport equations and the Euler equations have been presented. For the extension to viscous flow several techniques are investigated, ...

In this paper we discuss the numerical solution of initial-boundary value problem for the fourth order parabolic partial integro-differential equation. We use the forward Euler scheme for time discretization and the quasi-wavelet method for space discretization. Sometimes, we give a new method about the treatment of boundary condition. Numerical experiment is included to demonstrate the validit...