Adaptive Numerical Simulation of Dynamic Contact Problems

Abstract

We present a new approach for the space-time adaptive solution of dynamic contact problems. By combining ideas from the recently introduced residual-type a posteriori error estimator for static contact problems (Krause et al., An efficient and reliable residual-type a posteriori error estimator for the Signorini problem. Numer. Math. (2014), DOI: 10.1007/s00211-014-0655-8) and the novel discretization scheme with local impact detection (Krause and Walloth, A family of space-time connecting discretization schemes with local impact detection for elastodynamic contact problems. Comput. Methods Appl. Mech. Eng. 200:3425–3438, 2011), a discretization method is constructed which is able to detect and resolve local nonsmooth effects at the contact boundary in space and time. Numerical results in 3D illustrate our theoretical findings.