Advances in Differential Equations

Error estimates for a finite element discretization of the Cahn-Hilliard-Gurtin equations

Sami Injrou and Morgan Pierre

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Abstract

We prove optimal error estimates in energy norms and related norms for a space semidiscrete and for a fully discrete approximation of the Cahn-Hilliard-Gurtin equations with source terms. Numerical simulations in one and two space dimensions illustrate the theoretical results. We also prove convergence to equilibrium for the fully discrete scheme without source terms by the use of the Łojasiewicz inequality.

Article information

Source
Adv. Differential Equations Volume 15, Number 11/12 (2010), 1161-1192.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854438

Mathematical Reviews number (MathSciNet)
MR2743498

Zentralblatt MATH identifier
1227.65080

Subjects
Primary: 65M15: Error bounds 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65M12: Stability and convergence of numerical methods

Citation

Injrou, Sami; Pierre, Morgan. Error estimates for a finite element discretization of the Cahn-Hilliard-Gurtin equations. Adv. Differential Equations 15 (2010), no. 11/12, 1161--1192. https://projecteuclid.org/euclid.ade/1355854438.


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