A New Mixed Finite Element Method For The Cahn-Hilliard Equation
Zhen Liu, Rui Ma, Min Zhang
TL;DR
This paper introduces a novel mixed finite element method for the Cahn-Hilliard equation, establishing its well-posedness, error estimates, and demonstrating its efficiency and accuracy through numerical experiments in multiple dimensions.
Contribution
It presents a new unified mixed finite element approach for the Cahn-Hilliard equation applicable in 2D and 3D with arbitrary polynomial degrees.
Findings
Method is well-posed and stable.
Error estimates are rigorously derived.
Numerical experiments confirm accuracy and efficiency.
Abstract
This paper presents a new mixed finite element method for the Cahn-Hilliard equation. The well-posedness of the mixed formulation is established and the error estimates for its linearized fully discrete scheme are provided. The new mixed finite element method provides a unified construction in two and three dimensions allowing for arbitrary polynomial degrees. Numerical experiments are given to validate the efficiency and accuracy of the theoretical results.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Differential Equations and Numerical Methods · Solidification and crystal growth phenomena