A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity
Year: 2024
Author: Menghan Liu, Xiaoping Xie
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 221–243
Abstract
We consider a semi-discrete finite element method for a dynamic model for linear viscoelastic materials based on the constitutive law of fractional order. The corresponding integro-differential equation is of a Mittag-Leffler type convolution kernel. A 4-node hybrid stress quadrilateral finite element is used for the spatial discretization. We show the existence and uniqueness of the semi-discrete solution, then derive some error estimates. Finally, we provide several numerical examples to verify the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1009
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 2 : pp. 221–243
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Integro-differential equation fractional order viscoelasticity hybrid stress finite element error estimate.