ON GLOBAL SPATIAL REGULARITY AND CONVERGENCE RATES FOR TIME-DEPENDENT ELASTO-PLASTICITY
Dorothee Knees · Mathematical Models and Methods in Applied Sciences · 2010
We study the global spatial regularity of solutions of generalized elasto-plastic models with linear hardening on smooth domains. Under natural smoothness assumptions on the data and the boundary we obtain u ∈ L ∞ ((0, T); H 3/2-δ (Ω)) for the displacements and z ∈ L ∞ ((0, T); H 1/2-δ (Ω)) for the internal variables. The proof relies on a reflection argument which gives the regularity result in directions normal to the boundary on the basis of tangential regularity results. Based on the regularity results we derive convergence rates for a finite element approximation of the models.