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Approximation to a parabolic system modeling the thermoelastic contacts of two rods
Author(s) -
Zhao Jennifer J.
Publication year - 1998
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/(sici)1098-2426(199801)14:1<1::aid-num1>3.0.co;2-u
Subject(s) - thermoelastic damping , mathematics , norm (philosophy) , partial differential equation , rod , finite difference , sequence (biology) , mathematical analysis , parabolic partial differential equation , thermal , thermodynamics , physics , medicine , alternative medicine , genetics , pathology , biology , political science , law
In this article, we study a sequence of finite difference approximate solutions to a parabolic system, which models two dissimilar rods that may come into contact as a result of thermoelastic expansion. We construct the approximate solutions based on a set of finite difference schemes to the system, and we will prove that the approximate solutions converge strongly to the exact solutions. Moreover, we obtain and prove rigorously the error bound, which measures the difference between the exact solutions and approximate solutions in a reasonable norm. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:1–25, 1998