A posteriori error estimation for elasto-plastic problems based on duality theory. (English) Zbl 0886.73082

We introduce a new approach to a posteriori error estimation for elasto-plastic problems based on the duality theory of the calculus of variations. We show that, in spite of the prevailing view, duality methods provide a viable way for obtaining computable a posteriori error estimates for nonlinear boundary value problems without directly solving the dual problem. Rigorous mathematical analysis leads to what we call duality error estimators consisting of two parts: the error in the constitutive law and the error in the equilibrium equations. The duality error estimators hold for any conforming approximation of the exact solution regardless of whether or not they satisfy the Galerkin orthogonality condition. In particular, they encompass the familiar smoothening or gradient averaging techniques commonly used in practice.


74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
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