David Aristoff's homepage Title: Two modes of locking in poroelasticity: Causes and remedies

Abstract: In this talk, I will discuss two modes of locking phenomena in poroelasticity: Possion locking and pressure oscillations. I will first study the regularity of the solution of the Biot model to gain some insight into the cause of Poisson locking and show that the displacement gets into a divergence-free state as the Lam\'{e} constant $\lambda$ approaches $\infty$.Then, I will examine the cause of pressure oscillations from an algebraic point of view when a three-field mixed finite element method is used. Based on the results of my study on the causes of the two modes of locking, I will propose a new family of mixed finite elements that are free of both pressure oscillations and Poisson locking. Some numerical results will be presented to validate our theoretical studies.