Continuous data assimilation and long-time accuracy in a \(C^0\) interior penalty method for the Cahn-Hilliard equation

We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The method uses a C\(^0\) interior penalty spatial discretization of the fourth order Cahn-Hilliard equations, together with a backward E...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Diegel, Amanda E, Rebholz, Leo G
Format: Article
Language:English
Subjects:
Approximation
Data assimilation
Discretization
Initial conditions
Mathematical analysis
Online Access:Get full text
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Summary:We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The method uses a C\(^0\) interior penalty spatial discretization of the fourth order Cahn-Hilliard equations, together with a backward Euler temporal discretization. We prove the method is long time stable and long time accurate, for arbitrarily inaccurate initial conditions, provided enough data measurements are incorporated into the simulation. Numerical experiments illustrate the effectiveness of the method on a benchmark test problem.
ISSN:2331-8422