Convergence Analysis of Non-conforming Finite Element Method for a Quasi-static Contact Problem

doi:10.1007/s42967-024-00459-x

Abstract

Abstract: We analyze the numerical solution of a non-linear evolutionary variational inequality, which is encountered in the investigation of quasi-static contact problems. The study of this article encompasses both the semi-discrete and fully discrete schemes, where we employ the backward Euler method for time discretization and utilize the lowest order Crouzeix-Raviart non-conforming finite-element method for spatial discretization. By assuming appropriate regularity conditions on the solution, we establish a priori error analysis for these schemes, achieving the optimal convergence order for linear elements. To illustrate the numerical convergence rates, we provide numerical results on a two-dimensional test problem.

Key words: Finite-element method, A priori error estimates, Variational inequalities, Quasi-static problem, Supremum norm

CLC Number:

Kamana Porwal, Tanvi Wadhawan. Convergence Analysis of Non-conforming Finite Element Method for a Quasi-static Contact Problem[J]. Communications on Applied Mathematics and Computation, 2026, 8(2): 578-604.

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