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

✍ Scribed by Takehiko Kinoshita; Mitsuhiro T. Nakao

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 650 KB
• Volume: 234
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.12.044

✦ Synopsis

We present constructive a priori error estimates for H 2 0 -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 H 2 0projection 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]).