ANALYSIS FOR TIME DISCRETE APPROXIMATIONS OF BLOW-UP SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS

被引：15

作者：

Kyza, Irene ^{[1
]}

Makridakis, Charalambos ^{[2
,3
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Univ Crete, Dept Appl Math, Iraklion 71409, Greece

[3] FORTH, Inst Appl & Computat Math, Iraklion 71110, Greece

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 01期

关键词：

semilinear parabolic equations; blow-up solutions and rate; conditional a posteriori estimates; backward Euler method; Crank-Nicolson method; reconstruction technique; energy techniques; fixed point arguments; Duhamel's principle; POSTERIORI ERROR ANALYSIS; CRANK-NICOLSON METHOD; BEHAVIOR;

D O I：

10.1137/100796819

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a posteriori error estimates for time discrete approximations, for semilinear parabolic equations with solutions that might blow up in finite time. In particular we consider the backward Euler and the Crank-Nicolson methods. The main tools that are used in the analysis are the reconstruction technique and energy methods combined with appropriate fixed point arguments. The final estimates we derive are conditional and lead to error control near the blow up time.

引用

页码：405 / 426

页数：22

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