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The pointwise estimates of a conservative difference scheme for Burgers' equation
Author(s) -
Zhang Qifeng,
Wang Xuping,
Sun Zhizhong
Publication year - 2020
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.22494
Subject(s) - mathematics , pointwise , norm (philosophy) , a priori and a posteriori , bounded function , burgers' equation , a priori estimate , mathematical analysis , convergence (economics) , nonlinear system , partial differential equation , philosophy , epistemology , political science , law , economics , economic growth , physics , quantum mechanics
In this article, we are concerned with the numerical analysis of a nonlinear implicit difference scheme for Burgers' equation. A priori estimation of the analytical solution is provided in the sense of L ∞ ‐norm when the initial value is bounded in H 1 ‐norm. Conservation, boundedness, and unique solvability are proved at length. Inspired by the method of the priori estimation for the analytical solution, we prove the convergence and stability of the difference scheme in L ∞ ‐norm. Finally, numerical examples are carried out to verify our theoretical results.