Finite Element Scheme with H2N2 Interpolation for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation
Year: 2024
Author: Huiqin Zhang, Yanping Chen, Jianwei Zhou, Yang Wang
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 5 : pp. 1197–1222
Abstract
In this paper, two numerical schemes for the multi-term fractional mixed diffusion and diffusion-wave equation (of order $α,$ with $0<α<2$) 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 $3−α.$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0117
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 5 : pp. 1197–1222
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: The multi-term fractional mixed diffusion and diffusion-wave equation finite element method H2N2 interpolation fast algorithm stability and convergence.