Keller-Segel模型的不连续Galerkin近似的后验误差控制

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2024-12-13 DOI:10.1007/s10444-024-10212-w

Jan Giesselmann, Kiwoong Kwon

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引用次数: 0

摘要

给出了二维或三维抛物-椭圆型Keller-Segel系统的不连续Galerkin格式的后测误差估计。估计是有条件的，因为后验可计算量需要足够小，这可以通过网格细化来保证；估计是最优的，因为误差估计器的衰减顺序与网格细化下的误差相同。我们的误差估计器的一个特点是，它可以用来证明一个弱解的存在到一定时间的数值结果。

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A posteriori error control for a discontinuous Galerkin approximation of a Keller-Segel model

We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional in the sense that an a posteriori computable quantity needs to be small enough—which can be ensured by mesh refinement—and optimal in the sense that the error estimator decays with the same order as the error under mesh refinement. A specific feature of our error estimator is that it can be used to prove the existence of a weak solution up to a certain time based on numerical results.

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.