Second-Order, Fully Decoupled, Linearized, and Unconditionally Stable Scalar Auxiliary Variable Schemes for Cahn-Hilliard-Darcy System

Abstract

In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn-Hilliard-Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods have the features of second order accuracy, totally decoupling, linearization, and unconditional energy stability. The unconditionally stability of the two proposed decoupled numerical schemes are rigorously proved. Abundant numerical results are reported to verify the accuracy and effectiveness of proposed numerical methods.

Department(s)

Mathematics and Statistics

Publication Status

Early View: Online Version of Record before inclusion in an issue

Comments

Xiaoming He is partially supported by the NSF grants DMS-1722647

First published 17 Aug 2021

Keywords and Phrases

Cahn-Hilliard-Darcy System; Finite Element Method; Fully Decoupled; Scalar Auxiliary Variable Approach; Second-Order; Unconditional Stability

International Standard Serial Number (ISSN)

1098-2426; 0749-159X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Wiley, All rights reserved.

Publication Date

17 Aug 2021

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