Journal article

Hessian recovery based finite element methods for the Cahn-Hilliard equation

Minqiang Xu, Hailong Guo, Qingsong Zou

JOURNAL OF COMPUTATIONAL PHYSICS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2019

Abstract

In this paper, we propose several novel recovery based finite element methods for the 2D Cahn-Hilliard equation. One distinguishing feature of those methods is that we discretize the fourth-order differential operator in a standard C0 linear finite elements space. Precisely, we first transform the fourth-order Cahn-Hilliard equation to its variational formulation in which only first-order and second-order derivatives are involved and then we compute the first and second-order derivatives of a linear finite element function by a least-squares fitting recovery procedure. When the underlying mesh is uniform meshes of regular pattern, our recovery scheme for the Laplacian operator coincides with..

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University of Melbourne Researchers

Grants

Awarded by NSFC


Awarded by special project high performance computing of National Key Research and Development Program


Awarded by Guangdong Provincial NSF


Funding Acknowledgements

This author was partially supported by the NSFC 11571384.This author was partially supported by Andrew Sisson Fund of the University of Melbourne.This author was partially supported by the special project high performance computing of National Key Research and Development Program 2016YFB0200604, NSFC 11571384, and Guangdong Provincial NSF 2017B030311001.