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A New Mixed Finite Element Method for Elastodynamics with Weak Symmetry

A New Mixed Finite Element Method for Elastodynamics with Weak Symmetry We provide a new mixed finite element analysis for linear elastodynamics with reduced symmetry. The problem is formulated as a second order system in time by imposing only the Cauchy stress tensor and the rotation as primary and secondary variables, respectively. We prove that the resulting variational formulation is well-posed and provide a convergence analysis for a class of $${\mathrm {H}}(\mathop {{\mathrm {div}}}\nolimits )$$ H ( div ) -conforming semi-discrete schemes. In addition, we use the Newmark trapezoidal rule to obtain a fully discrete version of the problem and carry out the corresponding convergence analysis. Finally, numerical tests illustrating the performance of the fully discrete scheme are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

A New Mixed Finite Element Method for Elastodynamics with Weak Symmetry

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References (24)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
DOI
10.1007/s10915-017-0384-0
Publisher site
See Article on Publisher Site

Abstract

We provide a new mixed finite element analysis for linear elastodynamics with reduced symmetry. The problem is formulated as a second order system in time by imposing only the Cauchy stress tensor and the rotation as primary and secondary variables, respectively. We prove that the resulting variational formulation is well-posed and provide a convergence analysis for a class of $${\mathrm {H}}(\mathop {{\mathrm {div}}}\nolimits )$$ H ( div ) -conforming semi-discrete schemes. In addition, we use the Newmark trapezoidal rule to obtain a fully discrete version of the problem and carry out the corresponding convergence analysis. Finally, numerical tests illustrating the performance of the fully discrete scheme are presented.

Journal

Journal of Scientific ComputingSpringer Journals

Published: Feb 17, 2017

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