Abstract: A class of one-dimensional impact and dynamic contact problems taking into account non-smooth velocities is studied. The new space-time finite element approximation of dynamic variational inequalities is suggested. The non-smooth solution for the impact of an obstacle by an elastic bar and its energy conservation under persistency conditions is proved on partitions of the space-time domain. The explicit solution of the double impact problem is taken as an analytical benchmark for numerical experiments. For an iterative solution, a primal-dual active set (PDAS) algorithm stemming from semi-smooth Newton methods is constructed. Numerical experiments compare the space-time PDAS method with some other existing methods: a mass redistribution method, Paoli–Schatzman scheme, and a Nitsche-based approximation, highlighting its advantages.

Cite: Kovtunenko V.A. , Petrov A. , Renard Y.
Space-time FEM solution of dynamic contact problem with discontinuous velocity for multiple impact of deformed bar using PDAS method
Mathematical Methods in the Applied Sciences. 2025. 0:1 :1-16. DOI: 10.1002/mma.70370 WOS Scopus

Dates:

Submitted:	Aug 21, 2025
Accepted:	Nov 19, 2025
Published print:	Dec 7, 2025

Identifiers:

Web of science:	WOS:001631753800001
Scopus:	2-s2.0-105024087852

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