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SUMMARY:Asymptotic modeling of composite materials with thin coatings by u
 sing complex variables - Sonia Mogilevskaya (University of Minnesota)
DTSTART:20191212T140000Z
DTEND:20191212T143000Z
UID:TALK135616@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Co-Authors: Svetlana Baranova (University of Minnesota) Domini
 k Schillinger and Hoa Nguyen (Leibniz Universit&auml\;t Hannover&#xFFFD\;)
 <br> <br> Recent advances in surface chemistry made it possible to create 
 materials with ultrathin high-performance coating layers. Numerical modeli
 ng of such structures is a challenging task\, as accurate resolution of th
 in layers with standard continuum-based numerical methods\, e.g. FEM or BE
 M\, would require prohibitively fine mesh sizes. To avoid this\, it has be
 en proposed in the literature to replace a finite-thickness coating layer 
 by an interface of zero thickness and model the associated jump conditions
  in the relevant fields. The existing models\, however\, are low order acc
 urate with respect to the thickness of the layer. The reasons for this con
 siderable limitation are related to theoretical difficulties in constructi
 ng accurate higher-order interface models and to computational difficultie
 s in integrating these models into standard FEM formulations characterized
  by low regularity conditions for the involved fields and geometry.<br> <b
 r> This talk presents a) a new complex variables based approach in develop
 ing arbitrary orders interface models for two-dimensional potential proble
 ms involving thin isotropic interphase layers and b) a new variationally c
 onsistent FEM discretization framework to naturally deal with higher-order
  derivatives on complex surfaces. Theoretical and computational benefits o
 f the proposed approach will be discussed.
LOCATION:Seminar Room 1\, Newton Institute
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