We present an abstract framework for treating the theory of well-posedness of solutions to
abstract parabolic partial di¤ erential equations on evolving Hilbert spaces. This theory is …

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 consider existence and uniqueness for several examples of linear parabolic equations
formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation …

In this article we present a one-field monolithic finite element method in the Arbitrary
Lagrangian–Eulerian (ALE) formulation for Fluid–Structure Interaction (FSI) problems. The …

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

We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete
schemes of any order applied to an advection–diffusion model defined on moving domains …

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 …

We study the numerical approximation of partial differential equations with random input
data. Such problems arise when the uncertainty of the underlying system is taken into …