Erratum to “finite Element Approximation of the Cahn-hilliard-cook Equation”
نویسندگان
چکیده
We prove an additional result on the linearized Cahn-HilliardCook equation to fill in a gap in the main argument in our paper which was published in SIAM J. Numer. Anal. 49 (2011), 2407–2429. The result is a pathwise error estimate, which is proved by an application of the factorization argument for stochastic convolutions.
منابع مشابه
Finite Element Approximation of the Linearized Cahn-hilliard-cook Equation
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. The backward Euler time stepping is also studied. The analysis is set in a framework based on analytic semigroups. The main part ...
متن کاملErratum: Finite Element Approximation of the Cahn-Hilliard-Cook Equation
We prove an additional result on the linearized Cahn-HilliardCook equation to fill in a gap in the main argument in our paper which was published in SIAM J. Numer. Anal. 49 (2011), 2407–2429. The result is a pathwise error estimate, which is proved by an application of the factorization argument for stochastic convolutions.
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We study the nonlinear stochastic Cahn-Hilliard equation driven 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.
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An error bound is proved for a fully practical piecewise linear nite element approximation, using a backward Euler time discretization, of the Cahn-Hilliard equation with a logarithmic free energy.
متن کاملA Posteriori Error Estimates for Finite Element Approximations of the Cahn-hilliard Equation and the Hele-shaw Flow
This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut + ∆ ` ε∆u− ε−1f(u) ́ = 0. It is shown that the a posteriori error bounds depends on ε−1 only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct an adaptive algorithm f...
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تاریخ انتشار 2014