IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Ninth Annual Graduate Student Mini-conference in Computational Mathematics

Alistair Bentley
Clemson University
https://mthsc.clemson.edu/directory/view_person.py?person_id=364
Abstract

Inf-Sup stable finite elements for axisymmetric linear elasticity

  • Feb. 17, 2018
  • 2:40 p.m.
  • LeConte 412

In science and engineering, many three-dimensional processes have an axisymmetric solution profile. In these cases, the problem can be recast in cylindrical coordinates and decoupled into a pair of two-dimensional problems. In turn, this dimension reduction significantly reduces the computational effort needed to approximate the solution.

Despite considerable progress developing finite elements over the past decade, it appears that no inf-sup stable finite elements have been developed for the axisymmetric linear elasticity problem. In this presentation, I discuss the development of a computational framework for the axisymmetric linear elasticity problem. In particular, I review the methods used to build stable linear elasticity finite elements in Cartesian coordinates and explain why these approaches donÕt work in cylindrical coordinates. Moreover, I introduce a modification to the axisymmetric linear elasticity problem that appears to permit a family of inf-sup stable finite elements.

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