5 citations · 7 across the 11 of their papers we have counts for
13 papers
Trace inequalities for piecewise functions over general polytopic meshes
Michele Botti, Lorenzo Mascotto
Trace inequalities are crucial tools to derive the stability of partial differential equations with inhomogeneous, natural boundary conditions. In the analysis of corresponding Gal…
A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation
Zhaonan Dong, Emmanuil H. Georgoulis, Lorenzo Mascotto +1
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The…
A generalized Hessian-based error estimator for an IPDG formulation of the biharmonic problem in two dimensions
Théophile Chaumont-Frelet, Joscha Gedicke, Lorenzo Mascotto
We consider a two dimensional biharmonic problem and its discretization by means of a symmetric interior penalty discontinuous Galerkin method. A novel split of an error measure ba…
Sobolev-Poincaré inequalities for piecewise functions over general polytopic meshes
Michele Botti, Lorenzo Mascotto
We establish Sobolev-Poincaré inequalities for piecewise functions over families of fairly general polytopic (thence also shape-regular simplicial and Cartesian) meshes i…
New Crouzeix-Raviart elements of even degree: theoretical aspects, numerical performance, and applications to the Stokes' equations
Andrea Bressan, Lorenzo Mascotto, Marialetizia Mosconi
We construct new Crouzeix-Raviart (CR) spaces of even degree that are spanned by basis functions mimicking those for the odd degree case. Compared to the standard CR gospel, th…
A priori and a posteriori error estimates of a -in-time method for the wave equation in second order formulation
Zhaonan Dong, Lorenzo Mascotto, Zuodong Wang
We establish fully-discrete a priori and semi-discrete in time a posteriori error estimates for a discontinuous-continuous Galerkin discretization of the wave equation in second or…
A Nečas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuška-Aziz inequality
Michele Botti, Lorenzo Mascotto
We prove a Nečas-Lions inequality with symmetric gradients on two and three dimensional domains of diameter that are star-shaped with respect to a ball of radius ; the const…
-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes
Zhaonan Dong, Lorenzo Mascotto
We prove hp-optimal error estimates for the original DG method when approximating solutions to first-order hyperbolic problems with constant convection fields in the L2 and DG norm…
-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem
Zhaonan Dong, Lorenzo Mascotto
We prove -optimal error estimates for interior penalty discontinuous Galerkin methods (IPDG) for the biharmonic problem with homogeneous essential boundary conditions. We consi…
On the suboptimality of the p-version discontinuous Galerkin methods for first order hyperbolic problems
Zhaonan Dong, Lorenzo Mascotto
We address the issue of the suboptimality in the p-version discontinuous Galerkin (dG) methods for first order hyperbolic problems. The convergence rate is derived for the upwind d…
Stability analysis of polytopic Discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems
Paola F. Antonietti, Lorenzo Mascotto, Marco Verani +1
We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-…
Residual-based a posteriori error estimates for -discontinuous Galerkin discretisations of the biharmonic problem
Zhaonan Dong, Lorenzo Mascotto, Oliver J. Sutton
We introduce a residual-based a posteriori error estimator for a novel -version interior penalty discontinuous Galerkin method for the biharmonic problem in two and three dimen…
A multigrid algorithm for the -version of the Virtual Element Method
P. F. Antonietti, L. Mascotto, M. Verani
We present a multigrid algorithm for the solution of the linear systems of equations stemming from the version of the Virtual Element discretization of a two-dimensional Poisso…