We study finite element approximations of stochastic partial differential equations of Ginzburg-Landau type and the main paradigm considered in this paper is the stochastic Allen-Cahn model. We first demonstrate that the constructed stochastic finite element approximations are within an arbitrary level of tolerance from the corresponding one-dimensional stochastic partial differential equation;...

A formal asymptotic analysis of two classes of phase field models for void growth and coarsening in irradiated solids has been performed to assess their sharp-interface kinetics. It was found that the sharp interface limit of type B models, which include only point defect concentrations as order parameters governed by Cahn-Hilliard equations, captures diffusion-controlled kinetics. It was also ...

This paper addresses the approximation of surface diffusion flow using Cahn–Hilliard-type models. We introduce and analyze a new variational phase field model that associates classical Cahn–Hilliard energy with two degenerate mobilities guarantees second-order accuracy in sharp limit. also simple efficient numerical schemes to approximate solutions three models for flow, including one we propos...

In this paper, we establish a Stroock-Varadhan support theorem for the global mild solution to a d (d ≤ 3)-dimensional stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise.

We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre's theorem and unconditional von Neumann stability analysis, both of which we present. Numerical tests confirm the accuracy of the von Neumann approach, which is straightforward and sho...

We present an efficient scheme within the phase field framework for imposing dynamic contact angle boundary conditions for wall-bounded flows of two immiscible incompressible fluids with large density ratios. First, we develop an algorithm for imposing the dynamic contact angle boundary conditions to the Cahn–Hilliard equation. Our algorithm consists of two components: (i) we ignore the boundar...

The gradient flow approach to the Cahn-Hilliard and phase field models is developed, and some basic mathematical properties of the models, especially phase separation phenomena, are reviewed.