A POSTERIORI ERROR ESTIMATES FOR THE TWO-STEP BACKWARD DIFFERENTIATION FORMULA METHOD FOR PARABOLIC EQUATIONS

被引：22
|
作者：
Akrivis, Georgios [1 ]
Chatzipantelidis, Panagiotis [2 ]
机构：
[1] Univ Ioannina, Dept Comp Sci, GR-45110 Ioannina, Greece
[2] Univ Crete, Dept Math, Iraklion 71409, Greece
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2010年 / 48卷 / 01期
关键词：
parabolic equations; two-step backward differentiation formula method; residual; two-step backward differentiation formula reconstruction; a posteriori error analysis; CRANK-NICOLSON METHOD;
D O I：
10.1137/090756995
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We derive optimal order residual-based a posteriori error estimates for time discretizations by the two-step backward differentiation formula (BDF) method for linear parabolic equations. Appropriate reconstructions of the approximate solution play a key role in the analysis. To utilize the BDF method we employ one step by both the trapezoidal method or the backward Euler scheme. Our a posteriori error estimates are of optimal order for the former choice and suboptimal for the latter. Simple numerical experiments illustrate this behavior.
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页码：109 / 132
页数：24
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