3 citations · 4 across the 9 of their papers we have counts for
12 papers
Resonant solutions and (in)stability of the linear wave equation
Giancarlo Sangalli, Davide Terazzi, Pietro Zanotti
We revise the analysis of the acoustic wave equation, addressing the question whether the classical well-posedness implies the existence of an isomorphism between prescribed soluti…
Strictly equivalent a~posteriori error estimators for quasi-optimal nonconforming methods
Christian Kreuzer, Matthias Rott, Andreas Veeser +1
We devise a posteriori error estimators for quasi-optimal nonconforming finite element methods approximating symmetric elliptic problems of second and fourth order. These estimator…
Pressure robust finite element discretizations of the nonlinear Stokes equations
Lars Diening, Adrian Hirn, Christian Kreuzer +1
We present first-order nonconforming Crouzeix-Raviart discretizations for the nonlinear generalized Stokes equations with -structure. Thereby the velocity-errors are indepen…
Inf-sup stable discretization of the quasi-static Biot's equations in poroelasticity
C. Kreuzer, P. Zanotti
We propose a new full discretization of the Biot's equations in poroelasticity. The construction is driven by the inf-sup theory, which we recently developed. It builds upon the fo…
Inf-sup theory for the quasi-static Biot's equations in poroelasticity
C. Kreuzer, P. Zanotti
We analyze the two-field formulation of the quasi-static Biot's equations in bounded domains by means of the inf-sup theory. For this purpose, we exploit an equivalent four-field f…
Quasi-optimal and pressure robust discretizations of the Stokes equations by moment- and divergence-preserving operators
Christian Kreuzer, Rüdiger Verfürth, Pietro Zanotti
We approximate the solution of the Stokes equations by a new quasi-optimal and pressure robust discontinuous Galerkin discretization of arbitrary order. This means quasi-optimality…
A quasi-optimal variant of the Hybrid High-Order method for elliptic PDEs with loads
Alexandre Ern, Pietro Zanotti
Hybrid High-Order methods for elliptic diffusion problems have been originally formulated for loads in the Lebesgue space . In this paper we devise and analyze a variant th…
Quasi-optimal and pressure robust discretizations of the Stokes equations by new augmented Lagrangian formulations
Christian Kreuzer, Pietro Zanotti
We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based o…
A Quasi-Optimal Crouzeix-Raviart Discretization of the Stokes Equations
Rüdiger Verfürth, Pietro Zanotti
We present a modification of the Crouzeix-Raviart discretization of the Stokes equations in arbitrary dimension which is quasi-optimal, in the sense that the error of the discrete…
Quasi-optimal nonconforming methods for symmetric elliptic problems. III -- DG and other interior penalty methods
Andreas Veeser, Pietro Zanotti
We devise new variants of the following nonconforming finite element methods: DG methods of fixed arbitrary order for the Poisson problem, the Crouzeix-Raviart interior penalty met…
Quasi-optimal nonconforming methods for symmetric elliptic problems. II -- Overconsistency and classical nonconforming elements
Andreas Veeser, Pietro Zanotti
We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions int…
Quasi-optimal nonconforming methods for symmetric elliptic problems. I -- Abstract theory
Andreas Veeser, Pietro Zanotti
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optim…