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.
Esta prepublicacion dio origen a la(s) siguiente(s) publicación(es) definitiva(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).