Numerical Solution of Parabolic Problems Based on a Weak Space-Time Formulation
Numerical Solution of Parabolic Problems Based on a Weak Space-Time Formulation
复制标题
基于弱时空公式的抛物型问题的数值求解
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
M. Molteni
中科院分区：
文献类型：
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作者：
S. Larsson;M. Molteni
摘要我们研究了热方程的弱时空表述及其用于构造数值格式的方法。该制剂是基于一个已知的弱时空制剂，与不同的是，一个逐点分量的解决方案，这在其他作品通常被忽略，现在保持。我们首先使用这样的分量来获得解的逐点界，然后部署它来构造数值方案，从而研究这样的分量的作用。所得到的格式除了在L2 ${L^{2}}$意义下是拟最优的外，在时间节点上也是逐点超收敛的.我们证明了先验误差估计，我们提出了数值实验，以经验支持我们的研究结果。
Abstract We investigate a weak space-time formulation of the heat equation and its use for the construction of a numerical scheme. The formulation is based on a known weak space-time formulation, with the difference that a pointwise component of the solution, which in other works is usually neglected, is now kept. We investigate the role of such a component by first using it to obtain a pointwise bound on the solution and then deploying it to construct a numerical scheme. The scheme obtained, besides being quasi-optimal in the L 2 ${L^{2}}$ sense, is also pointwise superconvergent in the temporal nodes. We prove a priori error estimates and we present numerical experiments to empirically support our findings.