A posteriori error estimates for finite element discretizations of the heat equation
A posteriori error estimates for finite element discretizations of the heat equation
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DOI：
10.1007/s10092-003-0073-2
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发表时间：
2003-12
期刊：
影响因子：
1.7
通讯作者：
R. Verfürth
中科院分区：
文献类型：
--
作者：
R. Verfürth
我们考虑在时间上用A-稳定的θ-格式离散热传导方程，在空间上用协调元离散热传导方程。对于这些离散化，我们得到残留的后验误差指标。这些指标产生在空间和时间上是全局的误差的上界，并产生在空间上是全局的、在时间上是局部的误差的下界。上下界之间的比率在时间上是一致有界的，并且不依赖于空间或时间上的任何步长。此外，在空间和时间上的步长之间的关系没有限制。
We consider discretizations of the heat equation by A-stableθ-schemes in time and conforming finite elements in space. For these discretizations we derive residual a posteriori error indicators. The indicators yield upper bounds on the error which are global in space and time and yield lower bounds that are global in space and local in time. The ratio between upper and lower bounds is uniformly bounded in time and does not depend on any step-size in space or time. Moreover, there is no restriction on the relation between the step-sizes in space and time.