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On a finite element approximation for the elastoplastic torsion problem. (English) Zbl 1502.65192

Summary: This study is concerned with the elastoplastic torsion problem and its standard finite element approximation using piecewise affine Lagrange finite elements. In the case of a polytopal convex domain in dimension \(n = 1,2, 3\) we obtain an \(H^1\)-error bound of order \(h\) for the solution. For a nonconvex domain, we obtain also an error estimate.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
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
35Q74 PDEs in connection with mechanics of deformable solids
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