Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
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DOI：
10.1090/s0025-5718-06-01858-8
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发表时间：
2006-05
期刊：
影响因子：
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通讯作者：
O. Lakkis;C. Makridakis
中科院分区：
文献类型：
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作者：
O. Lakkis;C. Makridakis
本文给出了线性抛物型方程解的全离散逼近的后验误差估计。空间离散化使用允许随时间变化的有限元空间。我们的主要工具是一个适当的适应椭圆重建技术，介绍了Makridakis和Nochetto。我们得到了L∞（0，T; L2（Ω））和高阶空间L∞（0，T;H1（Ω））和H1（0，T; L2（Ω））的范数的新的后验估计，并给出了最优收敛阶.
We derive a posteriori error estimates for fully discrete approximations to solutions of linear parabolic equations. The space discretization uses finite element spaces that are allowed to change in time. Our main tool is an appropriate adaptation of the elliptic reconstruction technique, introduced by Makridakis and Nochetto. We derive novel a posteriori estimates for the norms of L∞(0, T; L2(Ω)) and the higher order spaces, L∞(0, T;H1(Ω)) and H1(0, T; L2(Ω)), with optimal orders of convergence.