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Numerical solution to a one‐dimensional thermoplastic problem with unilateral constraint
Author(s) -
Zhao Lei,
Sun Zhizhong,
Liu Jianming
Publication year - 2006
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.20144
Subject(s) - mathematics , convergence (economics) , constraint (computer aided design) , polygon mesh , reduction (mathematics) , stability (learning theory) , partial differential equation , numerical analysis , obstacle , space (punctuation) , numerical stability , mathematical analysis , geometry , computer science , political science , law , economics , machine learning , economic growth , operating system
In this article, we present a numerical simulation of one‐dimensional problem of quasi‐static contact with an elastic obstacle. A finite difference scheme is derived by the method of reduction of order on uniform meshes. The stability and convergence are proved. The convergence order is of O (τ 2 + h 2 ), where τ and h are the time step size and the space step size, respectively. Some numerical examples demonstrate the theoretical results. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005