TY - JOUR

T1 - On very accurate enclosure of the optimal constant in the a priori error estimates for H0
2-projection

AU - Kinoshita, Takehiko

AU - Nakao, Mitsuhiro T.

PY - 2010/5/15

Y1 - 2010/5/15

N2 - We present constructive a priori error estimates for H0
2-projection into a space of polynomials on a one-dimensional interval. Here, "constructive" indicates that we can obtain the error bounds in which all constants are explicitly given or are represented in a numerically computable form. Using the properties of Legendre polynomials, we consider a method by which to determine these constants to be as small as possible. Using the proposed technique, the optimal constant could be enclosed in a very narrow interval with result verification. Furthermore, constructive error estimates for finite element H0
2-projection in one dimension are presented. These types of estimates will play an important role in the numerical verification of solutions for nonlinear fourth-order elliptic problems as well as in the guaranteed a posteriori error analysis for the finite element method or the spectral method (e.g. Hashimoto et al. (2006) [2], Nakao et al. (2008) [3], Watanabe et al. (2009) [11]).

AB - We present constructive a priori error estimates for H0
2-projection into a space of polynomials on a one-dimensional interval. Here, "constructive" indicates that we can obtain the error bounds in which all constants are explicitly given or are represented in a numerically computable form. Using the properties of Legendre polynomials, we consider a method by which to determine these constants to be as small as possible. Using the proposed technique, the optimal constant could be enclosed in a very narrow interval with result verification. Furthermore, constructive error estimates for finite element H0
2-projection in one dimension are presented. These types of estimates will play an important role in the numerical verification of solutions for nonlinear fourth-order elliptic problems as well as in the guaranteed a posteriori error analysis for the finite element method or the spectral method (e.g. Hashimoto et al. (2006) [2], Nakao et al. (2008) [3], Watanabe et al. (2009) [11]).

KW - Constructive a priori error estimates

KW - Fourth-order elliptic problem

KW - Legendre polynomials

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U2 - 10.1016/j.cam.2009.12.044

DO - 10.1016/j.cam.2009.12.044

M3 - Article

AN - SCOPUS:77649271494

VL - 234

SP - 526

EP - 537

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -