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Numerical study of unbounded capillary surfaces
Department of Applied Mathematics University of Waterloo 200 University Ave. West Waterloo N2L 3G1 Canada. (Pharmacometrics Group)ORCID iD: 0000-0002-5881-2023
2014 (English)In: Pacific Journal of Mathematics, ISSN 0030-8730, E-ISSN 1945-5844, Vol. 267, no 1, 1-34 p.Article in journal (Refereed) Published
Abstract [en]

Unbounded capillary surfaces in domains with a sharp corner or a cusp are studied. It is shown how numerical study using a proposed computational methodology leads to two new conjectures for open problems on the asymptotic behavior of capillary surfaces in domains with a cusp. The numerical methodology contains two simple but important ingredients, a change of variable and a change of coordinates, which are inspired by known asymptotic approximations for unbounded capillary surfaces. These ingredients are combined with the finite volume element or Galerkin finite element methods. Extensive numerical tests show that the proposed computational methodology leads to a global approximation method for singular solutions of the Laplace–Young equation that recovers the proper asymptotic behavior at the singular point, is more accurate and has better convergence properties than numerical methods considered for singular capillary surfaces before. Using this computational methodology, two open problems on the asymptotic behavior of capillary surfaces in domains with a cusp are studied numerically, leading to two conjectures that may guide future analytical work on these open problems.

Place, publisher, year, edition, pages
2014. Vol. 267, no 1, 1-34 p.
Keyword [en]
singularity, asymptotic analysis, nonlinear elliptic PDE, Laplace–Young equation, finite element method
National Category
Computational Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-244410DOI: 10.2140/pjm.2014.267.1OAI: oai:DiVA.org:uu-244410DiVA: diva2:788751
Available from: 2015-02-16 Created: 2015-02-16 Last updated: 2017-12-04Bibliographically approved

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Aoki, Yasunori

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