Convergence Analysis And EFG Of A Quasistatic Frictionless Contact Problem For Viscoelastic Long Memory Material With Normal Compliance

Element-free Galerkin method(EFG)is a meshfree method based on weak form.This method has the advantage of high numerical accuracy and stability and it's the most popular meshfree method.EFG is introduced in detail and it's applied to solve boundary value problems of a class of elliptic PDEs and the quasistatic frictionless contact problems for viscoelastic long memory materials with normal compliance.The main contents in this paper are as follows:1.It introduces EFG method for the boundary value problems of one class elliptic PDEs and presents the numerical algorithm for EFG.It demonstrates the efficiency of EFG method by some numerical examples.It discusss the effect to numerical results under different domains,different boundary conditions and different weight functions.2.It introduces the quasistatic frictionless contact problems for viscoelastic long memory materials with normal compliance.The physical background and variational formulation of quasistatic contact problem is given in detail.The existence and uniqueness of the quasistatic contact problem is proved.3.Using the MLS approximation,time difference and complex trapezoidal integral formulation,it constructed the EFG full-discrete scheme for the quasistatic frictionless contact problems for viscoelastic long memory materials with normal compliance.EFG numerical framework for contact problem is discussed.The error estimation and convergence analysis of EFG full-discrete scheme is provided.Three numerical examples are realized to verify the efficiency and convergence result of EFG method.The numerical results demonstrate that the numerical convergence order is agreed with the ones of theoretical estimation.