Fast algorithm for viscous Cahn-Hilliard equation

doi:10.1007/s11464-021-0974-x

Front. Math. China

2022, Vol. 17

Issue (4) : 689-713 https://doi.org/10.1007/s11464-021-0974-x

RESEARCH ARTICLE

Fast algorithm for viscous Cahn-Hilliard equation

Danxia WANG(

), Yaqian LI, Xingxing WANG, Hongen JIA

College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

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Abstract

The main purpose of this paper is to solve the viscous Cahn-Hilliard equation via a fast algorithm based on the two time-mesh (TT-M) finite element (FE) method to ease the problem caused by strong nonlinearities. The TT-M FE algorithm includes the following main computing steps. First, a nonlinear FE method is applied on a coarse time-mesh τ_c. Here, the FE method is used for spatial discretization and the implicit second-order θ scheme (containing both implicit Crank-Nicolson and second-order backward difference) is used for temporal discretization. Second, based on the chosen initial iterative value, a linearized FE system on time fine mesh is solved, where some useful coarse numerical solutions are found by Lagrange’s interpolation formula. The analysis for both stability and a priori error estimates is made in detail. Numerical examples are given to demonstrate the validity of the proposed algorithm. Our algorithm is compared with the traditional Galerkin FE method and it is evident that our fast algorithm can save computational time.

Keywords Fast algorithm two time-mesh (TT-M) finite element (FE) method viscous Cahn-Hilliard equation stability CPU time

Corresponding Author(s): Danxia WANG

Issue Date: 19 December 2022

Cite this article:

Danxia WANG,Yaqian LI,Xingxing WANG, et al. Fast algorithm for viscous Cahn-Hilliard equation[J]. Front. Math. China, 2022, 17(4): 689-713.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0974-x
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I4/689

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