A finite element method for the Cahn-Hilliard equation (a semilinear parabolic equation of fourth order) is analyzed, both in a spatially semidisCrete case and in a completely discrete case based on the backward Euler method. Error bounds of optimal order over a finite time interval are obtained for solutions with smooth and nonsmooth initial data. A detailed study of the regularity of the exac...

ABSTRACT. In this paper, a numerical method is constructed for solving one-dimensional time dependent modified Burgers’ equation for various values of Reynolds number. At high Reynolds number, an inviscid boundary layer is produced in the neighborhood of right part of the lateral surface of the domain and the problem can be considered as a non-linear singularly perturbed problem involving a sma...

Problems associated with dendritic crystallization requires careful implementation of numerical methods. In the past few years various methods have been developed [F.Gibou et al., 2003; F.Gibou and R.Fedkiw, 2005] to track topologically complex, solid-liquid interface in crystal growth simulation. In this work we employ gradient augmented level set method [Nave et al., 2010] to track interface....

We present simulations of diffusion-limited transport in an initially cold medium of two different materials subjected to an impulsive radiative load, using a Newton-Krylov-Schwarz solver. The spatial discretization employs Galerkin finite elements with linear piecewise continuous basis functions over simplices in 2D and 3D. Temporal integration is via a solution-adaptive implicit Euler method....

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...

A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations. The time discretization of the penalty Navier-Stokes equations is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Navier-Stokes equations is based on a finite element space pair (Xh,Mh) which satisfies some approximate assumpt...

This letter presents a novel cascade ΣΔ modulator architecture that employs inter-stage resonation to increase its effective resolution compared to traditional cascades while presenting very relaxed output swing requirements and, subsequently, high robustness to non-linearities of the amplifiers. In addition, the use of loop filters based on Forward-Euler integrators, instead of Backward-Euler ...

In this paper, a nonconforming mixed finite element method (FEM) is presented to approximate time-dependent Maxwell’s equations in a three-dimensional bounded domain with absorbing boundary conditions (ABC). By employing traditional variational formula, instead of adding penalty terms, we show that the discrete scheme is robust. Meanwhile, with the help of the element’s typical properties and d...

Two midpoint-trapezoid pairs of dynamically equivalent (conjugate) algorithms are derived as compositions of first-order forward Euler and backward Euler integrators as applied to an incremental form of the initial-value problem of three-dimensional rigid body rotation. The algorithms are related to the recently developed methodology of the so-called Munthe-Kaas Runge–Kutta methods. Selected ex...

In this paper, we investigate an a posteriori error estimate of a control constrained optimal control problem governed by a time-dependent convection diffusion equation. Control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method or by adding a Moreau-Yosida-type penalty function to the cost functional. An adaptive mesh refinement indicated by a ...