Variational mesh adaptation II: error estimates and monitor functions |
| |
| Affiliation: | 1. Department of Mathematics, The University of Kansas, Lawrence, KS 66045, USA;2. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, PR China;1. Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy;2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany;1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China;2. School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology (QUT), GPO Box 2434, Brisbane, QLD 4001, Australia;1. Center for Advanced Vehicular Systems and Department of Mechanical Engineering, Mississippi State University, USA |
| |
| Abstract: | The key to the success of a variational mesh adaptation method is to define a proper monitor function which controls mesh adaptation. In this paper we study the choice of the monitor function for the variational adaptive mesh method developed in the previous work [J. Comput. Phys. 174 (2001) 924]. Two types of monitor functions, scalar matrix and non-scalar matrix ones, are defined based on asymptotic estimates of interpolation error obtained using the interpolation theory of finite element methods. The choice of the adaptation intensity parameter is also discussed for each of these monitor functions. Asymptotic bounds on interpolation error are obtained for adaptive meshes that satisfy the regularity and equidistribution conditions. Two-dimensional numerical results are given to verify the theoretical findings. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
