TY - JOUR
T1 - A Hybrid Stress Finite Element Method for Integro-Differential Equations Modelling Dynamic Fractional Order Viscoelasticity
AU - Liu , Menghan
AU - Xie , Xiaoping
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 221
EP - 243
PY - 2024
DA - 2024/04
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1009
UR - https://global-sci.org/intro/article_detail/ijnam/23025.html
KW - Integro-differential equation, fractional order viscoelasticity, hybrid stress finite element, error estimate.
AB - <p style="text-align: justify;">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.</p>