摘要
In this paper,numerical analysis is carried out for a class of history-dependent variationalhemivariational inequalities by arising in contact problems.Three different numerical treatments for temporal discretization are proposed to approximate the continuous model.Fixed-point iteration algorithms are employed to implement the implicit scheme and the convergence is proved with a convergence rate independent of the time step-size and mesh grid-size.A special temporal discretization is introduced for the history-dependent operator,leading to numerical schemes for which the unique solvability and error bounds for the temporally discrete systems can be proved without any restriction on the time step-size.As for spatial approximation,the finite element method is applied and an optimal order error estimate for the linear element solutions is provided under appropriate regularity assumptions.Numerical examples are presented to illustrate the theoretical results.
基金
supported by National Natural Science Foundation of China(Grant Nos.11671098 and 91630309)
Higher Education Discipline Innovation Project(111 Project)(Grant No.B08018)
Institute of Scientific Computation and Financial Data Analysis,Shanghai University of Finance and Economics for the support during his visit。
