Fully discrete pointwise smoothing error estimates for measure valued initial data
Fully discrete pointwise smoothing error estimates for measure valued initial data
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测量值初始数据的完全离散逐点平滑误差估计
DOI：
10.1051/m2an/2023076
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Wagner, Jakob
中科院分区：
文献类型：
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作者：
Leykekhman, Dmitriy;Vexler, Boris;Wagner, Jakob
本文分析了正则Borel测度空间中一类初值齐次抛物问题。该问题在时间上用任意阶的间断Galerkin格式离散，在空间上用一阶或二阶连续有限元离散。我们展示了连续，半离散和完全离散问题的抛物光滑结果。我们的主要结果是在子域中支持初始数据的情况下，在结束时的估计的误差估计。为了得到这些结果，我们还给出了L2初值和二次有限元的误差估计，推广了作者以前对线性有限元建立的相应结果.
In this paper we analyze a homogeneous parabolic problem with initial data in the space of regular Borel measures. The problem is discretized in time with a discontinuous Galerkin scheme of arbitrary degree and in space with continuous finite elements of orders one or two. We show parabolic smoothing results for the continuous, semidiscrete and fully discrete problems. Our main results are interiorL∞error estimates for the evaluation at the endtime, in cases where the initial data is supported in a subdomain. In order to obtain these, we additionally show interiorL∞error estimates forL2initial data and quadratic finite elements, which extends the corresponding result previously established by the authors for linear finite elements.