2013
DOI: 10.1051/m2an/2013070
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A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

Abstract: Abstract. We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed pre… Show more

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Cited by 5 publications
(5 citation statements)
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“…[21,38,3]). (3) Some robust multilevel methods to solve the linear elasticity problem can be found in [16,40,25,31,20]. By constructing stable intergrid transfer operators similar to I h H , it is feasible to construct corresponding multilevel solvers to the hybridized mixed method.…”
Section: Proof It Follows Directly From Theorem 41 and Norm Equivalen...mentioning
confidence: 99%
“…[21,38,3]). (3) Some robust multilevel methods to solve the linear elasticity problem can be found in [16,40,25,31,20]. By constructing stable intergrid transfer operators similar to I h H , it is feasible to construct corresponding multilevel solvers to the hybridized mixed method.…”
Section: Proof It Follows Directly From Theorem 41 and Norm Equivalen...mentioning
confidence: 99%
“…• In [12] efficient solvers are analyzed for IP approximations of linear elasticity problems, considering all cases: the pure displacement, the mixed and the traction free problems. The last two cases pose some extra pitfalls in the analysis since the spectral equivalence property (29) does not hold in those cases.…”
Section: Orthogonal Space Splittings In a Nutshellmentioning
confidence: 99%
“…This seems to be the only approach available till now, to prove convergence for the solvers of the nonsymmetric Interior Penalty methods. While the methodology has been applied to the lowest order DG space and conforming meshes, it is valid in two and three dimensions, and has already been adapted and extended to a larger family of problems: elliptic with jump coefficients [13]; linear elasticity [12]; and convection dominated problems corresponding to drift-diffusion models for transport of species [14].…”
Section: Introductionmentioning
confidence: 99%
“…Optimal multilevel preconditioners based on an orthogonal space decomposition of the DG space, were introduced in [16] for symmetric and non-symmetric piecewise linear IP approximations of elliptic problems. This technique has been adapted and extended to deal with a larger family of problems including elliptic problems with jumping coefficients [14], linear elasticity [13] and convection dominated problems corresponding to drift-diffusion models for the transport of species [15].…”
Section: Introductionmentioning
confidence: 99%