Fully discrete pointwise smoothing error estimates for measure valued initial data

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-09-06 DOI:10.1051/m2an/2023076

Boris Vexler, Dmitriy Leykekhman, Jakob Wagner

引用次数: 0

Abstract

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 interior $L^\infty$ 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 interior $L^\infty$ error estimates for $L^2$ initial data and quadratic finite elements, which extends the corresponding result previously established by the authors for linear finite elements.

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测量值初始数据的完全离散点平滑误差估计

本文分析了正则Borel测度空间中具有初始数据的齐次抛物问题。该问题在时间上用任意次的不连续伽辽金格式离散，在空间上用一阶或二阶的连续有限元离散。我们给出了连续、半离散和全离散问题的抛物平滑结果。我们的主要结果是在子域中支持初始数据的情况下，在结束时评估的内部$L^\infty$误差估计。为了得到这些，我们还给出了$L^2$初始数据和二次元的内部$L^\infty$误差估计，扩展了作者先前对线性有限元建立的相应结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.