High Order Finite Element Calculations for the Cahn-Hilliard Equation
نویسندگان
چکیده
منابع مشابه
High order finite element calculations for the deterministic Cahn-Hilliard equation
In this work, we propose a numerical method based on high degree continuous nodal elements for the Cahn-Hilliard evolution. The use of the p-version of the finite element method proves to be very efficient and favorably compares with other existing strategies (C1 elements, adaptive mesh refinement, multigrid resolution, etc). Beyond the classical benchmarks, a numerical study has been carried o...
متن کاملFinite Element Approximation of the Cahn-Hilliard-Cook Equation
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.
متن کاملStability and Convergence of a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation
In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and unconditionally uniquely solvable. Furthermore, we show that the discrete phase variable is bounded in L∞ (0, T ;L∞) and the discrete chemical potential is bou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Scientific Computing
سال: 2011
ISSN: 0885-7474,1573-7691
DOI: 10.1007/s10915-011-9546-7