# A New Family of Mixed Finite Elements for the Linear Elastodynamic Problem

@article{Bcache2002ANF, title={A New Family of Mixed Finite Elements for the Linear Elastodynamic Problem}, author={{\'E}liane B{\'e}cache and Patrick Joly and Chrysoula Tsogka}, journal={SIAM J. Numer. Anal.}, year={2002}, volume={39}, pages={2109-2132} }

We construct and analyze a new family of quadrangular (in two dimensions) or cubic (in three dimensions) mixed finite elements for the approximation of elastic wave equations. Our elements lead to explicit schemes (via mass lumping), after time discretization, including in the case of anisotropic media. Error estimates are given for these new elements.

## 81 Citations

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The Newmark trapezoidal rule is used to obtain a fully discrete version of the problem and carry out the corresponding convergence analysis for a class of H(div)-conforming semi-discrete schemes.

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- 2015

This paper proposes and analyzes semi-discrete and fully discrete hybrid stress finite element methods for elastodynamic problems. A hybrid stress quadrilateral finite element approximation is used…

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- 2019

The proposed method uses H ( div ) -conforming virtual element space of order k ( k ≥ 1 ) for the stress and discontinuous piecewise-polynomial spaces of degree k for the velocity and rotation for time discretization.

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- Computer ScienceArXiv
- 2021

This paper considers semi-discrete and fully discrete mixed finite element discretizations for Maxwell-model-based problems of wave propagation in 2-dimensional linear viscoelastic solid. A large…

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- 2005

In this paper, we are interested in the modeling of wave propagation in viscoelastic media. We present a family of models which generalize the Zener’s model. We achieve its mathematical analysis:…

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