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.
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页码：940 / 955
页数：16
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