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**Harvard**

Mesforush, A. (2010) *Finite element approximation of the deterministic and the stochastic Cahn-Hilliard equation*. Göteborg : Chalmers University of Technology (Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, nr: 3078).

** BibTeX **

@book{

Mesforush2010,

author={Mesforush, Ali},

title={Finite element approximation of the deterministic and the stochastic Cahn-Hilliard equation},

isbn={978-91-7385-397-2},

abstract={This thesis consists of three papers on numerical approximation of the Cahn-Hilliard equation. The main part of the work is concerned with the Cahn-Hilliard equation perturbed by noise, also known as the Cahn-Hilliard-Cook equation. In the ﬁrst paper we consider the linearized Cahn-Hilliard-Cook equation and we discretize it 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 analysis is set in a framework based on analytic semigroups. The main part of the work consists of detailed error bounds for the corresponding deterministic equation. Time discretization by the implicit Euler method is also considered. In the second paper we study the nonlinear Cahn-Hilliard-Cook equation.
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. In the third paper the deterministic Cahn-Hilliard equation is considered.
A posteriori error estimates are proved for a space-time Galerkin ﬁnite element method by using the methodology of dual weighted residuals. We also derive a weight-free a posteriori error estimate in which the weights are condensed into one global stability constant. },

publisher={Institutionen för matematiska vetenskaper, matematik, Chalmers tekniska högskola,},

place={Göteborg},

year={2010},

series={Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 3078},

keywords={ﬁnite element, a priori error estimate, stochastic integral, mild solution, dual weighted residuals, a posteriori error estimate, additive noise, Wiener process, Cahn-Hilliard equation, existence, regularity, Lya- punov functional, stochastic convolution},

note={95},

}

** RefWorks **

RT Dissertation/Thesis

SR Electronic

ID 121426

A1 Mesforush, Ali

T1 Finite element approximation of the deterministic and the stochastic Cahn-Hilliard equation

YR 2010

SN 978-91-7385-397-2

AB This thesis consists of three papers on numerical approximation of the Cahn-Hilliard equation. The main part of the work is concerned with the Cahn-Hilliard equation perturbed by noise, also known as the Cahn-Hilliard-Cook equation. In the ﬁrst paper we consider the linearized Cahn-Hilliard-Cook equation and we discretize it 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 analysis is set in a framework based on analytic semigroups. The main part of the work consists of detailed error bounds for the corresponding deterministic equation. Time discretization by the implicit Euler method is also considered. In the second paper we study the nonlinear Cahn-Hilliard-Cook equation.
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. In the third paper the deterministic Cahn-Hilliard equation is considered.
A posteriori error estimates are proved for a space-time Galerkin ﬁnite element method by using the methodology of dual weighted residuals. We also derive a weight-free a posteriori error estimate in which the weights are condensed into one global stability constant.

PB Institutionen för matematiska vetenskaper, matematik, Chalmers tekniska högskola,

T3 Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 3078

LA eng

LK http://publications.lib.chalmers.se/records/fulltext/121426.pdf

OL 30