Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 200, Issue 21-22, Pages 1846-1865Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2011.02.008
Keywords
Adaptive computation; Convergence; Complexity; Density functional theory; Finite element; Nonlinear eigenvalue problem
Funding
- Funds for Creative Research Groups of China [11021101]
- National Basic Research Program of China [2011CB309703]
- National High Technology Research and Development Program of China [2009AA01A134]
- National Science Foundation of China [10871198, 10971059]
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In this paper, we study finite element approximations of a class of nonlinear eigenvalue problems arising from quantum physics. We derive both a priori and a posteriori finite element error estimates and obtain optimal convergence rates for both linear and quadratic finite element approximations. In particular, we analyze the convergence and complexity of an adaptive finite element method. In our analysis, we utilize certain relationship between the finite element eigenvalue problem and the associated finite element boundary value approximations. We also present several numerical examples in quantum physics that support our theory. (C) 2011 Elsevier B.V. All rights reserved.
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