An enhanced VEM formulation for plane elasticity

Overlapping Schwarz preconditioner for the mixed formulation of plane elasticity

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...

Preconditioning for the mixed formulation of linear plane elasticity

algorithm: variable V-cycle Let mk be the number of smoothings and assume that β0mk ≤ mk−1 ≤ β1mk , where 1 < β0 ≤ β1. Algorithm Let B1 = Λ −1 1 . Assuming Bk−1 : Σk−1 → Σk−1 be defined, define Bk : Σk → Σk as follows. Let g ∈ Σk and τ 0 = 0. (1) τ l = τ l−1 + Rk(g −Λkτ ) for l = 1, · · · , mk; (2) σk = τk + IkBk−1I t k(g −Λkτ k); (3) σ = σ + Rk(g −Λkσ ) for l = mk + 1, · · · , 2mk ; Set Bkg = ...

An alternative to the Kelvin decomposition for plane anisotropic elasticity

A Multigrid Preconditioner for the Mixed Formulation of Linear Plane Elasticity

In this paper, we develop a multigrid preconditioner for the discrete system of linear equations which results from the mixed formulation of the linear plane elasticity problem using the Arnold-Winther elements. This, in turn, can be reduced to the problem of finding a multigrid preconditioner for the form (·, ·)+(div ·,div ·) in the symmetric tensor space resulting from Arnold-Winther elements...

A New Mixed Formulation for Elasticity

In this paper we present a new mixed variational formulation for the problem of linear elastostatics. Our formulation is very similar to the classical HellingerReissner formulation, but appears superior for finite element discretization. To make plain the relation between the Hellinger-Reissner formulation and the present one, we consider first an elastic body occupying a region g? in Euclidean...