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A New Mixed Finite Element Method for Elastodynamics with Weak Symmetry

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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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Authors and Affiliations

  1. CI²MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Carlos García & Gabriel N. Gatica

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, Calvo Sotelo s/n, Oviedo, Spain

    Salim Meddahi

Authors
  1. Carlos García
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  2. Gabriel N. Gatica
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  3. Salim Meddahi
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Corresponding author

Correspondence to Salim Meddahi.

Additional information

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

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