We introduce a Robust version of the Variational Physics-Informed Neural Networks method
(RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov …

This monograph is based on my personal lecture notes for the graduate course on
Mathematical Theory of Finite Elements (EM394H) that I have been teaching at ICES (now …

Abstract The Discontinuous Petrov–Galerkin (DPG) method for high frequency wave
propagation problems is discussed. The DPG method, with its attractive uniform (mesh and …

The flexibility of the DPG methodology is exposed by solving the linear elasticity equations
under different variational formulations, including some with non-symmetric functional …

We present an efficient implementation of the double adaptivity algorithm of Cohen et
al.(2012) within the setting of the Petrov–Galerkin method with optimal test functions. We …

At the fully discrete setting, stability of the discontinuous Petrov–Galerkin (DPG) method with
optimal test functions requires local test spaces that ensure the existence of Fortin operators …

We propose an adaptive multigrid preconditioning technology for solving linear systems
arising from Discontinuous Petrov–Galerkin (DPG) discretizations. Unlike standard multigrid …

We establish an abstract space-time DPG framework for the approximation of linear waves
in heterogeneous media. The estimates are based on a suitable variational setting in the …

We propose a three dimensional Discontinuous Petrov-Galerkin Maxwell approach for
modeling Raman gain in fiber laser amplifiers. In contrast with popular beam propagation …

A finite element methodology for large classes of variational boundary value problems is
defined which involves discretizing two linear operators:(1) the differential operator defining …