Ninth Annual Graduate Student Miniconference in Computational Mathematics
Alistair Bentley
Clemson University https://mthsc.clemson.edu/directory/view_person.py?person_id=364 

Abstract 
InfSup stable finite elements for axisymmetric linear elasticity
In science and engineering, many threedimensional processes have an axisymmetric solution profile. In these cases, the problem can be recast in cylindrical coordinates and decoupled into a pair of twodimensional 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 infsup 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 donĂ•t work in cylindrical coordinates. Moreover, I introduce a modification to the axisymmetric linear elasticity problem that appears to permit a family of infsup stable finite elements. 