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Sobolev gradient type preconditioning for the Saint-Venant model of elasto-plastic torsion. (English) Zbl 1138.35089

The paper is concerned with the study of the Sobolev gradient type preconditioning for Saint-Venant model of elasto-plastic torsion. The proposed iterative solution of the arising nonlinear elliptic problem is achieved by combining the advantages of Laplacian preconditioners with the qualitatively favourable aspects of the strong formulation. Error estimate is given for the convergence of the method.

MSC:

35Q72 Other PDE from mechanics (MSC2000)
35J65 Nonlinear boundary value problems for linear elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74S05 Finite element methods applied to problems in solid mechanics
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