We study the nonlinear stochastic Cahn-Hilliard equation driven by additive colored noise. We show almost sure existence and regularity of solutions. We introduce spatial approximation by a standard finite element method and prove error estimates of optimal order on sets of probability arbitrarily close to 1. We also prove strong convergence without known rate.

We survey several applications of the differential equation method in different areas of discrete mathematics. We give examples of its use in the analysis of algorithms in random graph processes and random boolean formulae. We also briefly review the basic theorem of Wormald [77] used in the analysis, but we aim for simplicity and not for maximal generality. The primary goal of this survey is t...

The Cahn-Hilliard-Cook equation continues to be a useful model describing binary phase separation in systems such as alloys and other physical and chemical applications. We describe our investigation of this field equation and report on the various discretisation schemes we used to integrate the system in one-, twoand three-dimensions. We also discuss how the equation can be visualised effectiv...

The linearized Cahn-Hilliard-Cook equation is discretized in the spatial variables by a standard finite element method. Strong convergence estimates are proved under suitable assumptions on the covariance operator of the Wiener process, which is driving the equation. The backward Euler time stepping is also studied. The analysis is set in a framework based on analytic semigroups. The main part ...

The main purpose of this study is to develop a variational formulation for predicting structure behavior and accounting damage mechanics in metallic materials. Mechanical coupled thermomechanical models are used predict failure manufacturing processes. Ductile accompanied by significant amount plastic deformation structural components. Finite element simulation evolution ductile solids presente...

Because of their superior ballistic and mechanical properties, lightweight materials like titanium alloy Ti-6Al-4V and aluminum alloy AA5083-H116 have been frequently used for aerospace and military applications. Tests of ballistic limit velocity are limited by expensive nature of the experimental setup, and indeed, that can be resolved by adopting numerical simulations. Numerical study involvi...