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Volume 14, Issue 2
Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation

Hao Yuan & Xiaoping Xie

Adv. Appl. Math. Mech., 14 (2022), pp. 344-364.

Published online: 2022-01

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  • Abstract

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.

  • AMS Subject Headings

65N30, 65M60, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-344, author = {Yuan , Hao and Xie , Xiaoping}, title = {Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {2}, pages = {344--364}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0014}, url = {http://global-sci.org/intro/article_detail/aamm/20201.html} }
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 -

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.

Hao Yuan & Xiaoping Xie. (2022). Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation. Advances in Applied Mathematics and Mechanics. 14 (2). 344-364. doi:10.4208/aamm.OA-2021-0014
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