# 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

, Volume 72 (3) – Feb 17, 2017
31 pages

/lp/springer_journal/a-new-mixed-finite-element-method-for-elastodynamics-with-weak-Q0Pody68pC
Publisher
Springer US
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
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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