A New Mixed Finite Element Method for Elastodynamics with Weak Symmetry |
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Authors: | Carlos García Gabriel N Gatica Salim Meddahi |
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Affiliation: | 1.CI2MA and Departamento de Ingeniería Matemática,Universidad de Concepción,Concepción,Chile;2.Departamento de Matemáticas, Facultad de Ciencias,Universidad de Oviedo,Oviedo,Spain |
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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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