Optimal BV estimates for a discontinuous Galerkin method for linear elasticity

By Adrian J. Lew, Patrizio Neff, Deborah Sulsky, Magdalena Ortiz. 2004

97 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/9d85e8e8fd05b8fe7b709358a0f3ef38be1bdb0e

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

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 ”
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 general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications (2006, methodology): “At this point, an assumed form of the deformation gradients is adopted extending to finite deformations of solids the assumed scalar gradients in Brezzi et al [9], see also [11]: Fh = ∇0φh + Rφ̄h (JφhK) (25) where the tensorial operator Rφ̄h : L 2 (∂IB0h) → Sh is defined as: ∫ B0h Rφ̄h (JvK) : τdV0 ”
Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity: Motivation, formulation, and numerical examples (2008, methodology): “Standard stability estimates, such as those shown in [20,24], do not guarantee the coercivity of the method with β = 0.”
A discontinuous‐Galerkin‐based immersed boundary method (2008, methodology): “The specific discontinuous Galerkin method studied in this work is the one adopted previously by Lew and coworkers [42, 69] for nonlinear elasticity, which utilizes the Bassi–Rebay numerical fluxes [6].”
A discontinuous Galerkin formulation for classical and gradient plasticity. Part 2: Algorithms and numerical analysis (2007, unknown): “[31–33]).”
An explicit discontinuous Galerkin method for non‐linear solid dynamics: Formulation, parallel implementation and scalability properties (2008, unknown): “Recent efforts to exploit the advantages of DG methods in solid mechanics have included applications to linear [1] and nearly incompressible elasticity [2], beams and plates [3], shells [4], failure [5] and strain-gradient theories of damage [6, 7].”