Matematik Bölümü Semineri: Orsan Kılıçer (Texas A&M Universitesi)

Yeditepe Üniversitesi Matematik Bölümü Seminerleri kapsamında bu hafta yapılacak olan seminerimizin detayları aşağıdaki gibi olup ilgilenen herkes davetlidir. 

Konuşmacı: Orsan Kılıçer (Texas A&M Universitesi)

Başlık (İngilizce): Higher Order FEM for Surface Stokes Problems

Özet (İngilizce): This research focuses on developing a higher-order finite element method for solving the Surface Stokes Problem. Finite element methods face challenges due to the possible ill-posedness caused by Killing fields, and an $H^1$-conforming method cannot be constructed for merely $C^0$ discrete surfaces.

To address these difficulties, this work introduces a mass term into both the weak and strong formulations and employs an H(div)-conforming $BDM_k - P_{k-1}$ pair for velocity and pressure while using Lagrange interpolation for higher-order surface approximations.

The study analyzes discrete Korn-type inequalities, discrete inf-sup conditions, norm equivalencies on discrete and continuous surfaces, and both geometric and Galerkin errors associated with the proposed method.

Theoretical error estimates demonstrate sharp energy error convergence for velocity and $L^2$ error convergence for pressure, which align well with numerical results. However, in theory, a suboptimal $L^2$ velocity error estimate is observed due to geometric error limitations.

Overall, this research provides a stable finite element framework for solving the Surface Stokes Problem. The findings contribute to the numerical analysis of surface partial differential equations and offer a foundation for further improvements in geometric error estimation.

Date: Friday, August 15, 2025
Time: 13:00 Istanbul Time 
Place: Google Meet (link: TBA)