Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
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چکیده
منابع مشابه
Finite Element Approximation of the Cahn-Hilliard Equation with Degenerate Mobility
We consider a fully practical nite element approximation of the Cahn-Hilliard equation with degenerate mobility @u @t = r:(b(u) r(?u+ 0 (u))); where b() 0 is a diiusional mobility and () is a homogeneous free energy. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resul...
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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.
متن کاملFinite 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 consider the Cahn-Hilliard equation with a logarithmic free energy and non-degenerate concentration dependent mobility. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we prove an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions. Finally some numerical experiments are pres...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 1999
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142997331669