A Fully-Discrete Finite Element Scheme and Projection-Iteration Algorithm for a Dynamic Contact Problem with Multi-contact Zones and Unilateral Constraint - Cai, Dong-Ling; Hu, Jingyan; Xiao, Yi-Bin; Zeng, Ping; Zhou, Guanyu (Journal of scientific computing, 2023)
A fully discrete finite element scheme is proposed to solve the dynamic viscoelastic contact problem with multi-contact zones and unilateral constraints. We develop the well-posedness and error analysis of the nonlinear numerical scheme under appropriate assumptions on the regularity of the solution. Moreover, we provide a projection-iteration algorithm for computation and show the convergence. Several numerical experiments are carried out to validate the theoretical results.