Finite Element Scheme with H2N2 Interpolation for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation

被引：2

作者：

Zhang, Huiqin ^{[1
]}

Chen, Yanping ^{[1
]}

Zhou, Jianwei ^{[2
]}

Wang, Yang ^{[3
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Linyi Univ, Sch Math & Stat, Linyi 276005, Shandong, Peoples R China

[3] Hubei Normal Univ, Sch Math & Stat, Huangshi 435002, Hubei, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2024年 / 16卷 / 05期

基金：

中国国家自然科学基金;

关键词：

The multi-term fractional mixed diffusion and diffusion-wave equation; finite element method; fast algorithm; stability and convergence; H2N2; interpolation; APPROXIMATION; COEFFICIENT;

D O I：

10.4208/aamm.OA-2023-0117

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, two numerical schemes for the multi-term fractional mixed diffusion and diffusion-wave equation (of order alpha, with 0 < alpha < 2) are developed to solve the initial value problem. Firstly, we study a direct numerical scheme that uses quadratic Charles Hermite and Newton (H2N2) interpolation polynomials approximations in the temporal direction and finite element discretization in the spatial direction. We prove the stability of the direct numerical scheme by the energy method and obtain a priori error estimate of the scheme with an accuracy of order 3- alpha. In order to improve computational efficiency, a new fast numerical scheme based on H2N2 interpolation and an efficient sum-of-exponentials approximation for the kernels is proposed. Numerical examples confirm the error estimation results and the validity of the fast scheme.

引用

页码：1197 / 1222

页数：26

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