抛物型方程指数中点积分有限元法的后验误差估计

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-12-20 DOI:10.1002/mma.10641

Xianfa Hu, Wansheng Wang, Yonglei Fang

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引用次数: 0

摘要

本文建立了线性和半线性抛物型方程的完全离散逼近的后验误差估计。时间离散采用指数中点法，空间离散采用标准线性元。通过引入连续分段二次重构，推导了时间离散化的误差。通过插值估计来评估空间离散化的误差。利用能量技术，我们导出了基于残差的全离散近似的后验下界和上界。我们的理论结果得到了大量数值实验的支持。

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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A Posteriori Error Estimates for Exponential Midpoint Integrator Finite Element Method for Parabolic Equations

In this paper, a posteriori error estimates for the fully discrete approximation for linear and semilinear parabolic equations are established. The exponential midpoint method is used for the temporal discretization, and the spatial discretization takes the standard linear elements. By introducing a continuous piecewise quadratic reconstruction, the error of the temporal discretization is derived. The error of the spatial discretization is evaluated by the interpolation estimates. Using the energy technique, we derive residual-based a posteriori lower and upper bounds for the fully discrete approximation. Our theoretical results are supported by extensive numerical experiments.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.