Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions

被引：0

作者：

Muhamadiev, Ergash ^{[1
]}

Nazarov, Murtazo ^{[2
]}

机构：

[1] Vologda State Univ, Dept Informat Syst & Technol, Vologda, Russia

[2] Uppsala Univ, Dept Informat Technol, Div Comp Sci, Uppsala, Sweden

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 423卷 / 02期

关键词：

Inequality; Lagrange interpolation estimates; Finite elements; Scalar conservation laws; Convergence; COMPUTATIONAL FLUID-DYNAMICS; SCALAR CONSERVATION-LAWS; MEASURE-VALUED SOLUTIONS; NAVIER-STOKES EQUATIONS; COMPRESSIBLE EULER; CONVERGENCE; FORMULATION; SYSTEMS;

D O I：

10.1016/j.jmaa.2014.10.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper the interpolation inequality of Szepessy [12, Lemma 4.2] is revisited. The lower bound in the above reference is proven to be proportional to p(-2), where p is a polynomial degree, that goes fast to zero as p increases. We prove that the lower bound is proportional to ln(2)p which is an increasing function. Moreover, we prove that this estimate is sharp. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：940 / 955

页数：16

共 26 条

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