中科院数学与系统科学研究院

数学研究所

动力系统研讨班报告

 

 

报告人 胡凯博 博士(挪威奥斯陆大学)

  目:Poincare integrals for elasticity

  间:2018.08.24(星期五), 11:00-12:00

  点:数学院南楼N913

 要:

The elasticity complex (linearized Calabi complex) describes the displacement, linearized strain (metric), incompatibility (linearized curvature) and stress tensors in elasticity and continuum theory for crystal defects. For the elasticity complex, we construct explicit integral operators satisfying the null-homotopy relation, the Koszul type complex property and the polynomial preserving property. Such path integrals for the de Rham complex play a crucial role in the proof of the Poincare lemma, and have been used in the construction of finite element differential forms and in the regularity theory of Maxwell equations. The key of our construction is the Bernstein-Gelfand-Gelfand (BGG) construction, which has been recently used by Arnold, Falk and Winther in the study of finite element methods for elasticity. As a special case, this rather different approach gives the Cesaro-Volterra path integral formula in classical elasticity for strain tensors satisfying the Saint-Venant compatibility condition. This is a joint work with Snorre Christiansen and Espen Sande.

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