TY - JOUR
T1 - Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation
AU - Yuan , Hao
AU - Xie , Xiaoping
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 344
EP - 364
PY - 2022
DA - 2022/01
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2021-0014
UR - https://global-sci.org/intro/article_detail/aamm/20201.html
KW - Maxwell viscoelastic model, mixed finite element, semi-discrete and fully discrete,
error estimate, stability.
AB - <p style="text-align: justify;">Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic
solid. This mixed finite element framework allows the use of a large class of existing mixed conforming finite elements for elasticity in the spatial discretization. In the
fully discrete scheme, a Crank-Nicolson scheme is adopted for the approximation of
the temporal derivatives of stress and velocity variables. Error estimates of the semi-discrete and fully discrete schemes, as well as an unconditional stability result for the
fully discrete scheme, are derived. Numerical experiments are provided to verify the
theoretical results.</p>