Discontinuous Galerkin methods for non‐linear elasticity

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Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian (2008, unknown): “Such discrete gradients arise naturally in the formulation of dG approximations and have been used recently also in [6] for nonlinear elasticity and in [2] for nonlinear diffusion.”
Analysis of an HDG method for linear elasticity (2015, methodology): “Indeed, in the following few years, DG methods were devised for linear elasticity in 2004 [3], for incompressible and near incompressible elastic materials in 2002 [4] and 2006 [5], for Timoshenko beams in 2006 [6], for fourth-order problems in structural and continuum mechanics in 2002 [7] and 2005”
A new discontinuous Galerkin method for Kirchhoff–Love shells (2008, background): “In the general context of finite element formulations for elliptic problems, jump-discontinuities are allowed across element boundaries for the solution of linear elasticity [1], non-linear elasticity [2,3], and plasticity [4], resulting in one-field formulations where the displacement field is the ”
Compact embeddings of broken Sobolev spaces and applications (2009, background): “Ten Eyck & Lew (2006) used alifting operatordefined by ∫ Ω R(uh) · ϕh dx = − ∫ Γint∪∂Ω [[uh]] · {ϕh}ds, (1.5) where{ϕh} is a suitable average (flux) of the bi-valued functionϕh on the skeleton, to define Ih(uh) = ∫ Ω f (x, uh,∇uh + R(uh))dx + ∫ ΓN g(x, uh)ds + ∫ Γint h−1|[[uh]] | 2 ds+ ∫ ΓD h−1|uh…”