An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

A Complete Multiscale Modelling Approach for Polymer–Clay Nanocomposites

We present an innovative, multiscale computational approach to probe the behaviour of polymer–clay nanocomposites (PCNs). Our modeling recipe is based on 1) quantum/force‐field‐based atomistic simulation to derive interaction energies among all system components; 2) mapping of these values onto mesoscopic bead–field (MBF) hybrid‐method parameters; 3) mesoscopic simulations to determine system density distributions and morphologies (i.e., intercalated versus exfoliated); and 4) simulations at finite‐element levels to calculate the relative macroscopic properties. The entire computational procedure has been applied to two well‐known PCN systems, namely Nylon 6/Cloisite 20A and Nylon 6/Cloisite 30B, as test materials, and their mechanical properties were predicted in excellent agreement with the available experimental data. Importantly, our methodology is a truly bottom‐up approach, and no “learning from experiment” was needed in any step of the entire procedure.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.