Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains
upon extending the domain velocity from the boundary into the bulk with the purpose of …

We develop a unified theory for continuous-in-time finite element discretizations of partial
differential equations posed in evolving domains, including the consideration of equations …

We present a velocity-based moving mesh virtual element method for the numerical solution
of PDEs involving boundaries which are free to move. The virtual element method is used for …

We introduce a framework for the design of finite element methods for two-dimensional
moving boundary problems with prescribed boundary evolution that have arbitrarily high …

We present two approaches to constructing isoparametric Virtual Element Methods of
arbitrary order for linear elliptic partial differential equations on general two-dimensional …

This book highlights key computational challenges involved in the two-way coupling of
complex liquid-fluid interfaces. Including pivotal applications as examples, the text defines …

Abstract A Streamline Upwind Petrov–Galerkin (SUPG) finite element method for a
convection dominated transient convection-diffusion-reaction equation in time-dependent …

We present a unified analysis of finite element methods for problems with prescribed moving
boundaries. In particular, we study an abstract parabolic problem posed on a moving …

We propose a family of methods for simulating two‐dimensional incompressible, low
Reynolds number flow around a moving obstacle whose motion is prescribed. The methods …

The past few years have unfolded differently than I anticipated. When I started my PhD in
October of 2019, no one could have predicted the onset of the COVID-19 pandemic and the …