CAM Seminar

Speaker: Vladimir Yushutin
Affiliation: Clemson University

Title: On convergence of trace FEM approximations for surface Navier--Stokes equation

Abstract: Consider the surface Navier--Stokes equation  posed on a fixed surface $\Gamma$. Assume only that the forcing (and, consequently, the flow) is minimally regular - a prototypical situation for a coupling of the tangential momentum transport with other physical phenomena on $\Gamma$. In this talk I will prove convergence of continuous-in-time, stabilized Trace FEM approximations for this model following compactness arguments.

Trace FEM is an unfitted method for surface PDEs which uses a bulk, regular mesh of the ambient space. As a result  of this otherwise convenient discretization, one needs a stabilization to combat the unfittedness.  The main novelty of the work is a proper modification of the convential stabilization scheme which allows us to show the strong convergence of the traces of bulk discrete solutions to the exact solution on $\Gamma$ without any additional assumptions on regularity of the latter.