In certain polytopal domains Ω, in space dimension d= 2, 3, we prove exponential
expressivity with stable ReLU Neural Networks (ReLU NNs) in H 1 (Ω) for weighted analytic …

We present a new hp-version space-time discontinuous Galerkin (dG) finite element method
for the numerical approximation of parabolic evolution equations on general spatial meshes …

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain
with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft …

We design and analyze an adaptive hp-finite element method (hp hp-AFEM) in dimensions
n= 1, 2 n= 1, 2. The algorithm consists of iterating two routines: hp hp-NEARBEST finds a …

The goal of this paper is to establish exponential convergence of hp-version interior penalty
(IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of …

In a plane polygon P with straight sides, we prove analytic regularity of the Leray--Hopf
solution of the stationary, viscous, and incompressible Navier--Stokes equations. We …

We study the regularity in weighted Sobolev spaces of Schrödinger-type eigenvalue
problems, and we analyze their approximation via a discontinuous Galerkin (dG) hp finite …

We establish exponential convergence of conforming hp-version and spectral finite element
methods for second-order, elliptic boundary-value problems with constant coefficients and …

The aim of this paper is to present a new class of smoothness testing strategies in the
context of h p-adaptive refinements based on continuous Sobolev embeddings. In addition …

In this paper we propose a least-squares spectral element method for three dimensional
elliptic interface problems. The differentiability estimates and the main stability theorem …