基于相对能量估计的Cahn-Hilliard系统稳定性及离散误差分析

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-02-17 DOI:10.1051/m2an/2023017

Aaron Brunk, Egger Herbert, Oliver Habrich, M. Lukácová-Medvidová

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引用次数: 1

摘要

用相对能量估计的方法研究了具有浓度依赖迁移率的Cahn-Hilliard方程解对扰动的稳定性。作为该分析的副产品，在强解的现实正则性假设下，在连续水平上导出了弱-强唯一性原理。通过适当的空间和时间上的伽辽金近似，进一步几乎逐字继承了稳定性估计。这允许在某些投影误差方面推导离散误差的明确界限，并为半和完全离散近似方案建立最优顺序先验误差估计。为了说明理论结果，给出了数值试验。

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Stability and discretization error analysis for the Cahn-Hilliard system via relative energy estimates

The stability of solutions to the Cahn-Hilliard equation with concentration dependent mobility with respect to perturbations is studied by means of relative energy estimates. As a by-product of this analysis, a weak-strong uniqueness principle is derived on the continuous level under realistic regularity assumptions on strong solutions. The stability estimates are further inherited almost verbatim by appropriate Galerkin approximations in space and time. This allows to derive sharp bounds for the discretization error in terms of certain projection errors and to establish order-optimal a-priori error estimates for semi- and fully discrete approximation schemes. Numerical tests are presented for illustration of the theoretical results.

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.