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.     

MHD-to-PIC transition for modeling of conduction and opening in aplasma opening switch

The plasma opening switch (POS) is a critical element of some inductive-energy-storage pulsed-power generators. Detailed understanding of plasma redistribution and thinning during the POS conduction phase can be gained through magnetohydrodynamic fluid (MHD) simulations. As space-charge separation and kinetic effects become important late in the conduction phase (beginning of the opening phase), MHD methods become invalid and particle-in-cell (PIC) methods should be used. In this paper, the applicability of MHD techniques is extended into PIC-like regimes by including nonideal MHD phenomena such as the Hall effect and resistivity. The feasibility of the PIC technique is, likewise, extended into high-density, low-temperature-MHD-like regimes by using a novel numerical cooling algorithm. At an appropriate time, an MHD-to-PIC transition must be accomplished in order to accurately simulate the POS opening phase. The mechanics for converting MHD output into PIC input are introduced, as are the transition criteria determining when to perform this conversion. To establish these transition criteria, side-by-side MHD and PIC simulations are presented and compared. These separate simulations are then complemented by a proof-of-principle MHD-to-PIC transition, thereby demonstrating this MHD-to-PIC technique as a potentially viable tool for the simulation of POS plasmas. Practical limitations of the MHD-to-PIC transition method and applicability of the transition criteria to hybrid fluid-kinetic simulations are discussed     

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.