Overlapping Schwarz preconditioner for the mixed formulation of plane elasticity
نویسنده
چکیده
Recently a stable pair of finite element spaces for the mixed formulation of the plane elasticity system has been developed by Arnold and Winther. Here we construct a two-level overlapping Schwarz preconditioner for the resulting discrete system. Essentially, this reduces to finding an efficient preconditioner for the form (·, ·) + (div ·,div ·) in the symmetric tensor space H(div ,Ω). The main difficulty comes from the well known complexity of building preconditioners for the div operator. We solve it by taking a decomposition similar to the Helmholz decomposition. Both additive and multiplicative preconditioners are studied, and the conditioner numbers are shown to be uniform with respect to the mesh size.
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