最小残差法中一种方便的非齐次边界条件包含

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-03-22 DOI:10.48550/arXiv.2303.12555

R. Stevenson

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引用次数: 1

摘要

摘要非齐次本质边界条件可以附加到适定偏微分方程，从而得到组合变分公式。相应算子的域是域Ω上的Sobolev空间，PDE是在该域上提出的，而共域是空间的笛卡尔乘积，其中包括函数在¦ΒΩ\partial\Omega上的分数阶Sobolev空格。在本文中，构造了易于实现的最小残差离散化，该离散化从所使用的试验空间产生准最优逼近，其中完全避免了对分数阶Sobolev范数的评估。

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A Convenient Inclusion of Inhomogeneous Boundary Conditions in Minimal Residual Methods

Abstract Inhomogeneous essential boundary conditions can be appended to a well-posed PDE to lead to a combined variational formulation. The domain of the corresponding operator is a Sobolev space on the domain Ω on which the PDE is posed, whereas the codomain is a Cartesian product of spaces, among them fractional Sobolev spaces of functions on ∂ Ω \partial\Omega . In this paper, easily implementable minimal residual discretizations are constructed which yield quasi-optimal approximation from the employed trial space, in which the evaluation of fractional Sobolev norms is fully avoided.

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.