On Diagonal Dominance of FEM Stiffness Matrix of Fractional Laplacian and Maximum Principle Preserving Schemes for the Fractional Allen-Cahn Equation

Liu, Hongyan1; Sheng, Changtao2; Wang, Li-Lian2; Yuan, Huifang3,4

2021-01-07

10.1007/s10915-020-01363-1

JOURNAL OF SCIENTIFIC COMPUTING   影响因子和分区

0885-7474

1573-7691

In this paper, we study diagonal dominance of the stiffness matrix resulted from the piecewise linear finite element discretisation of the integral fractional Laplacian under global homogeneous Dirichlet boundary condition in one spatial dimension. We first derive the exact form of this matrix in the frequency space which is extendable to multi-dimensional rectangular elements. Then we give the complete answer when the stiffness matrix can be strictly diagonally dominant. As one application, we apply this notion to the construction of maximum principle preserving schemes for the fractional-in-space Allen-Cahn equation, and provide ample numerical results to verify our findings.

Diagonal dominance Maximum principle Integral fractional Laplacian Fractional-in-space Allen-Cahn equation 35B50 41A05 41A25 74S05

SCI ; EI

英语

通讯

Singapore MOE AcRF Tier 2 Grants["MOE2018-T2-1-059","MOE2017-T2-2-144"]

Mathematics

Mathematics, Applied

WOS:000610070100002

SPRINGER/PLENUM PUBLISHERS

20210209747864

Boundary conditions ; Finite element method ; Laplace transforms ; Maximum principle ; Piecewise linear techniques ; Stiffness

Mathematics:921 ; Materials Science:951

MATHEMATICS

Web of Science

1.Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China
2.Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore
3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
4.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

Liu, Hongyan,Sheng, Changtao,Wang, Li-Lian,et al. On Diagonal Dominance of FEM Stiffness Matrix of Fractional Laplacian and Maximum Principle Preserving Schemes for the Fractional Allen-Cahn Equation[J]. JOURNAL OF SCIENTIFIC COMPUTING,2021,86(2).

Liu, Hongyan,Sheng, Changtao,Wang, Li-Lian,&Yuan, Huifang.(2021).On Diagonal Dominance of FEM Stiffness Matrix of Fractional Laplacian and Maximum Principle Preserving Schemes for the Fractional Allen-Cahn Equation.JOURNAL OF SCIENTIFIC COMPUTING,86(2).

Liu, Hongyan,et al."On Diagonal Dominance of FEM Stiffness Matrix of Fractional Laplacian and Maximum Principle Preserving Schemes for the Fractional Allen-Cahn Equation".JOURNAL OF SCIENTIFIC COMPUTING 86.2(2021).