Finite element approximation of the Cahn-Hilliard-Cook equation

• We study the nonlinear stochastic Cahn–Hilliard equation perturbed 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Cahn–Hilliard–Cook equation

additive noise

Wiener process

existence

regularity

finite element

error estimate

strong convergence

error estimate

Publication and Content Type

ref (subject category)

art (subject category)