We propose and analyse new space-time Galerkin-Bubnov-type finite element formulations
of parabolic and hyperbolic second-order partial differential equations in finite time intervals …

This book is the third volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

We analyze Galerkin discretizations of a new well-posed mixed space–time variational
formulation of parabolic partial differential equations. For suitable pairs of finite element trial …

We study extensions of piecewise polynomial data prescribed on faces and possibly in
elements of a patch of simplices sharing a vertex. In the $ H^ 1$ setting, we look for functions …

We establish the existence of liftings into discrete subspaces of H (div) of piecewise
polynomial data on locally refined simplicial partitions of polygonal/polyhedral domains. Our …

In this work, an r-linearly converging adaptive solver is constructed for parabolic evolution
equations in a simultaneous space-time variational formulation. Exploiting the product …

We propose an efficient mesh adaptive method for the numerical solution of time-dependent
partial differential equations considered in the fixed space-time cylinder Ω×(0, T). We employ …

The Richards equation is commonly used to model the flow of water and air through soil,
and it serves as a gateway equation for multiphase flows through porous media. It is a …

We consider the a posteriori error analysis of fully discrete approximations of parabolic
problems based on conforming hp-finite element methods in space and an arbitrary order …

We analyze constrained and unconstrained minimization problems on patches of tetrahedra
sharing a common vertex with discontinuous piecewise polynomial data of degree p. We …