Finite-element approximation of the linearized Cahn-Hilliard-Cook equation
Artikel i vetenskaplig tidskrift, 2011

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. Backward Euler time stepping is also studied. The analysis is set in a framework based on analytic semigroups. The main effort is spent on proving detailed error bounds for the corresponding deterministic Cahn–Hilliard equation. The results should be interpreted as results on the approximation of the stochastic convolution, which is a part of the mild solution of the nonlinear Cahn–Hilliard–Cook equation.

stochastic convolution

backward Euler method

Wiener process

finite-element method

Cahn–Hilliard–Cook equation

strong convergence

mean square error estimate

Författare

Stig Larsson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Ali Mesforush

Shahrood University of Technology

IMA Journal of Numerical Analysis

0272-4979 (ISSN) 1464-3642 (eISSN)

Vol. 31 4 1315-1333

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

Styrkeområden

Materialvetenskap

DOI

10.1093/imanum/drq042