Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation

Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation

Year:    2022

Author:    Hao Yuan, Xiaoping Xie

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2021-0014

Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 2 : pp. 344–364

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Maxwell viscoelastic model mixed finite element semi-discrete and fully discrete error estimate stability.

Author Details

Hao Yuan

Xiaoping Xie