Carlos Garcia, Gabriel N. Gatica, Salim Meddahi:
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 $H(div)$-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.
This preprint gave rise to the following definitive publication(s):
Carlos GARCIA, Gabriel N. GATICA, Salim MEDDAHI: A new mixed finite element analysis of the elastodynamic equations. Applied Mathematics Letters, vol. 59, pp. 48-55, (2016).
Carlos GARCIA, Gabriel N. GATICA, Salim MEDDAHI: A new mixed finite element method for elastodynamics with weak symmetry. Journal of Scientific Computing, vol. 72, 3, pp. 1049-1079, (2017).