A weak Galerkin finite element scheme for the Cahn-Hilliard equation
نویسندگان
چکیده
منابع مشابه
Finite 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 کاملDiscontinuous Galerkin Finite Element Approximation of the Cahn-Hilliard Equation with Convection
The paper is concerned with the construction and convergence analysis of a discontinuous Galerkin finite element method for the Cahn–Hilliard equation with convection. Using discontinuous piecewise polynomials of degree p ≥ 1 and backward Euler discretization in time, we show that the order-parameter c is approximated in the broken L∞(H1) norm with optimal order, O(hp+ τ); the associated chemic...
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 کاملA discontinuous Galerkin method for the Cahn-Hilliard equation
A discontinuous Galerkin finite element method has been developed to treat the high-order spatial derivatives appearing in the Cahn–Hilliard equation. The Cahn–Hilliard equation is a fourth-order nonlinear parabolic partial differential equation, originally proposed to model phase segregation of binary alloys. The developed discontinuous Galerkin approach avoids the need for mixed finite elemen...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2018
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3369