Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces

Binhu Xia, Yibao Li and Zhong Li
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Binhu Xia: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
Yibao Li: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
Zhong Li: School of Humanities and Social Science, Xi’an Jiaotong University, Xi’an 710049, China

Mathematics, 2020, vol. 8, issue 9, 1-12

Abstract: This paper describes temporally second-order unconditionally stable direct methods for Allen–Cahn and conservative Allen–Cahn equations on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. We prove that the proposed schemes, which combine a linearly stabilized splitting scheme, are unconditionally energy-stable. The resulting system of discrete equations is linear and is simple to implement. Several numerical experiments are performed to demonstrate the performance of our proposed algorithm.

Keywords: Allen–Cahn equation; conservative Allen–Cahn equation; Laplace–Beltrami operator; triangular surface mesh; unconditionally energy-stable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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