2017/07/06 by Georgios E. Zouraris, Zouraris, Georgios E.
Computer Science · Materials Science · Engineering · #Advanced Mathematical Modeling in Engineering #Solidification and crystal growth phenomena #Advanced Numerical Methods in Computational Mathematics
paper · pdf · doi:10.48550/arxiv.1707.01968
We consider a model initial- and Dirichlet boundary- value problem for a\nlinearized Cahn-Hilliard-Cook equation, in one space dimension, forced by the\nspace derivative of a space-time white noise. First, we introduce a canvas\nproblem the solution to which is a regular approximation of the mild solution\nto the problem and depends on a finite number of random variables. Then,\nfully-discrete approximations of the solution to the canvas problem are\nconstructed using, for discretization in space, a Galerkin finite element\nmethod based on H2 piecewise polynomials, and, for time-stepping, an\nimplicit/explicit method. Finally, we derive a strong a priori estimate of the\nerror approximating the mild solution to the problem by the canvas problem\nsolution, and of the numerical approximation error of the solution to the\ncanvas problem.\n