Virtual element method for simplified friction problem. (English) Zbl 1524.65864

Wang, Fei; Wei, Huayi

Appl. Math. Lett. 85, 125-131 (2018).

Summary: This work aims at studying the virtual element method (VEM) to solve a simplified friction problem, which is a typical elliptic variational inequality of the second kind. An optimal error estimate is derived in the \(H^1\) norm for the lowest-order VEM. A numerical example is reported to demonstrate the theoretically predicted convergence order.

© Elsevier Ltd

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05	Finite element methods applied to problems in solid mechanics
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
65K15	Numerical methods for variational inequalities and related problems
74M10	Friction in solid mechanics
35A23	Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
35R09	Integro-partial differential equations
35J15	Second-order elliptic equations

Keywords:

variational inequality; polygonal meshes; optimal error estimate

Software:

FEALPy; GitHub; iFEM

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