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É. Bécache, P. Joly, C. Tsogka (2001)
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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 $${\mathrm {H}}(\mathop {{\mathrm {div}}}\nolimits )$$ 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.
Journal of Scientific Computing – Springer Journals
Published: Feb 17, 2017
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