An Analysis of New Mixed Finite Elements for the Approximation of Wave Propagation Problems

Éliane Bécache (1) , Patrick Joly (1) , Chrysoula Tsogka (1)

1 INRIA Rocquencourt

We construct and analyze a new family of rectangular (two-dimensional) or cubic (three-dimensional) mixed finite elements for the approximation of the acoustic wave equations. The main advantage of this element is that it permits us to obtain through mass lumping an explicit scheme even in an anisotropic medium. Nonclassical error estimates are given for this new element.

Mots clés: mixed finite elements; mass lumping; anisotropic waves

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Éliane Bécache, Patrick Joly, Chrysoula Tsogka. An Analysis of New Mixed Finite Elements for the Approximation of Wave Propagation Problems. SIAM Journal on Numerical Analysis, 2000, 37 (4), pp.1053 - 1084. ⟨10.1137/S0036142998345499⟩. ⟨hal-01443182⟩