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The element‐free Galerkin method for a quasistatic contact problem with the Tresca friction in elastic materials
Author(s) -
Ding Rui,
Shen Quan,
Huo Yuebin
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22519
Subject(s) - quasistatic process , mathematics , penalty method , galerkin method , finite element method , mathematical analysis , discontinuous galerkin method , convergence (economics) , mathematical optimization , structural engineering , physics , engineering , quantum mechanics , economics , economic growth
This paper is proposed for the error estimates of the element‐free Galerkin method for a quasistatic contact problem with the Tresca friction. The penalty method is used to impose the clamped boundary conditions. The duality algorithm is also given to deal with the non‐differentiable term in the quasistatic contact problem with the Tresca friction. The error estimates indicate that the convergence order is dependent on the nodal spacing, the time step, the largest degree of basis functions in the moving least‐squares approximation, and the penalty factor. Numerical examples demonstrate the effectiveness of the element‐free Galerkin method and verify the theoretical analysis.