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A new a posteriori error estimation for nonlinear time-dependent finite element analysis. (English) Zbl 0949.74067

Summary: An error on the constitutive law (labeled the dissipation error) is used to measure the quality of finite element computations of plastic and viscoplastic structures whose behavior is described by internal variables. This measure takes into account all the classical sources of error involved in the computation: the space discretization (the mesh), the time discretization, and the iterative technique used to solve the nonlinear discrete problem. More specifically, to quantify the quality of the space and time discretizations, two quantities, called indicators, are introduced. The efficiency of both the error and the indicators is shown for several examples.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K99 Thin bodies, structures
74C99 Plastic materials, materials of stress-rate and internal-variable type
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