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 \({\mathrm {H}}(\mathop {{\mathrm {div}}}\nolimits )\)-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.
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This work was partially supported by CONICYT-Chile through BASAL project CMM, Universidad de Chile; by project Anillo ACT1118 (ANANUM), Centro de Investigación en Ingeniería Matemática (CI\(^2\)MA), Universidad de Concepción; and by the Ministery of Education of Spain through the project MTM2013-43671-P.
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García, C., Gatica, G.N. & Meddahi, S. A New Mixed Finite Element Method for Elastodynamics with Weak Symmetry. J Sci Comput 72, 1049–1079 (2017). https://doi.org/10.1007/s10915-017-0384-0
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DOI: https://doi.org/10.1007/s10915-017-0384-0