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Existence and convergence results for the Galerkin approximation of an electronic density functional
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Langwallner, Bernhard, Ortner, Christoph and Süli, Endre (2010) Existence and convergence results for the Galerkin approximation of an electronic density functional. Mathematical Models and Methods in Applied Sciences, Volume 20 (Number 12). pp. 2237-2265. doi:10.1142/S021820251000491X ISSN 0218-2025.
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WRAP-M3AS-Paper-01-09-298.pdf - Accepted Version - Requires a PDF viewer. Download (596Kb) | Preview |
Official URL: http://dx.doi.org/10.1142/S021820251000491X
Abstract
We formulate and analyze a model for the study of finite clusters of atoms or localized defects in infinite crystals based on orbital-free density functional theory. We show that the resulting constrained optimization problem has a minimizer and we provide a careful analysis of the solvability of the associated Euler–Lagrange equation. Based on these results, and using tools from saddle-point theory and nonlinear analysis, we then show that a Galerkin discretization has a solution that converges to the correct limit.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Galerkin methods, Crystalline polymers -- Defects -- Mathematical models | ||||
Journal or Publication Title: | Mathematical Models and Methods in Applied Sciences | ||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
ISSN: | 0218-2025 | ||||
Official Date: | December 2010 | ||||
Dates: |
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Volume: | Volume 20 | ||||
Number: | Number 12 | ||||
Page Range: | pp. 2237-2265 | ||||
DOI: | 10.1142/S021820251000491X | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 20 December 2015 | ||||
Date of first compliant Open Access: | 20 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) |
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