A Discrete Differential Sequence for Elasticity Based upon Continuous Displacements

Patrice Hauret (1) , Frédéric Hecht (2)

1 Centre de Technologie de Ladoux
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations

The present paper introduces a mixed stress-displacement method for linear elastic- ity as an extension of the work performed by Christiansen [Numer. Math., 119 (2011), pp. 613–640] for computational relativity. Moreover, we establish self-adjointness in a special sense and perform numerical simulations to assess the relevance of the method, including comparison with the recent TDNNS [A. Sinwel, A New Family of Mixed Finite Elements for Elasticity, Ph.D. thesis, Linz Uni- versity, 2009], [A. Pechstein and J. Scho ̈berl, Math. Models Methods Appl. Sci., 21 (2011), pp. 1761– 1782] mixed formulation. Extensions to higher order approximations and nonlinear elasticity are also introduced.

Mots clés: mixed methods; elasticity; discrete differential methods; exact sequences

Domaines: Analyse numérique [cs.NA]

Patrice Hauret, Frédéric Hecht. A Discrete Differential Sequence for Elasticity Based upon Continuous Displacements . SIAM Journal on Scientific Computing, 2013, 35 (1), pp.24. ⟨10.1137/110848189⟩. ⟨hal-01358406⟩