混合方法与下特征值界

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2023-02-03 DOI:10.1090/mcom/3820

Dietmar Gallistl

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引用次数: 0

摘要

给出了与偏微分算子相关的对称正定特征值问题的混合有限元方法如何提供保证的下特征值界。该方法基于混合方案的经典兼容条件(包含核)和与紧嵌入相关的局部常数，这些常数通常是显式已知的。应用包括标量二阶椭圆算子，线性弹性，和Steklov特征值问题。

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Mixed methods and lower eigenvalue bounds

It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility condition (inclusion of kernels) of the mixed scheme and on local constants related to compact embeddings, which are often known explicitly. Applications include scalar second-order elliptic operators, linear elasticity, and the Steklov eigenvalue problem.

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来源期刊

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.