Seminar Event Detail


Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, April 29, 2022
Location:  Virtual (3:00 PM to 4:00 PM)

Title:  Finite element methods for moving boundary problems based on universal meshes

Abstract:   Partial differential equations posed on domains that change with time arise frequently in science and engineering. A typical example is the flow of a fluid around a moving obstacle, where one must solve the Navier-Stokes equations on the evolving domain occupied by the fluid. Conventional numerical methods for solving such problems typically use one of two approaches: construct a moving mesh for the moving domain, or immerse the moving domain in a fixed background mesh. In this talk, I'll discuss a different approach based on a "universal mesh": a background mesh that adapts to the geometry of the moving domain at all times by adjusting a few elements near the moving boundary. I'll explain how to construct high-order finite element discretizations of moving-boundary problems using this approach, and I'll present a framework for proving a priori error estimates for these discretizations.

Files:


Speaker:  Evan Gawlik
Institution:  University of Hawaii

Event Organizer:   Thomas Anderson    tganders@umich.edu

 

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