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.     

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.     

Flaw localization using the reassigned spectrogram on laser-generated and detected Lamb modes

Rapid, accurate inspection of metallic plates using broadband guided waves has traditionally been limited by the multi-mode, highly dispersive nature of these waves; current practice typically restricts either the type of mode generated or detected, and/or its frequency range. The current study presents an effective alternative procedure by combining a novel digital signal processing technique, the reassigned spectrogram, with laser generated and detected Lamb waves. The reassigned spectrogram is used to characterize the modal and frequency content of a single ultrasonic signal as a function of time, enabling a procedure to locate flaws in an aluminum plate specimen.