A convergent adaptive wavelet-Rothe method for elastoplastic hardening

This paper is concerned with the development of adaptive wavelet methods for the hardening problem in elastoplasticity. We propose a Rothe method using some implicit scheme in time. Then, we consider a standard elastic predictor-plastic corrector method. The (non-linear) correction is performed by some convergent scheme such as a Newton-Raphson iteration or suitable modifications of it. Thus, it remains to solve Helmholtz-type problems with varying right-hand sides. These are solved by the convergent adaptive wavelet method introduced by Cohen, Dahmen, and DeVore. In the plastic correction, the trial strain might have to be corrected according to pointwise formulated hardening conditions. We propose an adaptive corrector method based on biorthogonal B-splines. This allows a fully adaptive stress correction. We obtain an overall convergent method. Some preliminary numerical results are presented.