In this paper we carefully study the large time behaviour of u(t, x, y) := Ex,y f(Xt, Yt)− ∫ f dμ, where (Xt, Yt) is the solution of a stochastic Hamiltonian dissipative system with non gbally Lipschitz coefficients, μ its unique invariant law, and f a smooth function with polynomial growth at infinity. Our aim is to prove the exponential decay to 0 of u(t, x, y) and all its derivatives when t ...

In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider a...

The main di culty in the implementation of most standard implicit Runge-Kutta (IRK) methods applied to (sti ) ordinary di erential equations (ODE's) is to e ciently solve the nonlinear system of equations. In this article we propose the use of a preconditioner whose decomposition cost for a parallel implementation is equivalent to the cost for the implicit Euler method. The preconditioner is ba...

Using a slightly diierent discretization scheme in time and adapting the approach in Nochetto et al: (1998) for analysing the time discretization error in the backward Euler method, we improve on the error bounds derived in (i) Barrett and Blowey (1998) and (ii) Barrett and Blowey (1999c) for a fully practical piece-wise linear nite element approximation of a model for phase separation of a mul...

In this paper, a novel variational approach for multi-modal image registration based on consistent non-rigid transforms is proposed. The forward and backward transforms are computed in a variational framework simultaneously. A consistency energy is added into the variational registration framework and an iterative method assures that the forward and backward transforms are close approximate inv...

We prove a weak rate of convergence fully discrete scheme for stochastic Cahn--Hilliard equation with additive noise, where the spectral Galerkin method is used in space and backward Euler time. Compared Allen--Cahn type partial differential equation, error analysis here much more sophisticated due to presence unbounded operator front nonlinear term. To address such issues, novel direct approac...

The main goal of this research is to analyse the effect of angular velocity on stability and vibration of a simply supported Rayleigh rotating shaft. To this end, non-dimensional kinetic and potential energies are written while lateral vibration is considered. Finite element method is employed to discrete the formulations and Linear method is applied to analyse instability threshold of a rotati...

In this study, the solutions of Simplified Magnetohyrodynamics (SMHD) equations by finite element method are examined with nonlinear time relaxation term. The differential filter κ(|u-u ̅ |(u-u )) term is added to SMHD equations. Also Nonlinear Time Relaxation Model (SMHDNTRM) introduced. model discretized Backward-Euler (BE) obtain solutions. Moreover, stability proved. found unconditionally st...

For Ait–Sahalia-type interest rate model with Poisson jumps, we are interested in strong convergence of a novel time-stepping method, called transformed jump-adapted backward Euler method (TJABEM). Under certain hypotheses, the considered takes values positive domain. It is shown that TJABEM can preserve domain underlying problem. Furthermore, first-order recovered respect to Lp-error criterion...