Lorenzo Mascotto
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View article: A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation
A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation Open
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 method combines standard finite elements in space and conti…
View article: A generalized Hessian-based error estimator for an IPDG formulation of the biharmonic problem in two dimensions
A generalized Hessian-based error estimator for an IPDG formulation of the biharmonic problem in two dimensions Open
We consider a two dimensional biharmonic problem and its discretization by means of a symmetric interior penalty discontinuous Galerkin method. Based on the ``div-div'' complex, a novel split of an error measure based on a generalized Hess…
View article: Sobolev-Poincaré inequalities for piecewise $W^{1,p}$ functions over general polytopic meshes
Sobolev-Poincaré inequalities for piecewise $W^{1,p}$ functions over general polytopic meshes Open
We establish Sobolev-Poincaré inequalities for piecewise $W^{1,p}$ functions over sequences of fairly general polytopic (thence also shape-regular simplicial and Cartesian) meshes in any dimension; amongst others, they cover the case of st…
View article: Generalised gradients for virtual elements and applications to a posteriori error analysis
Generalised gradients for virtual elements and applications to a posteriori error analysis Open
We rewrite the standard nodal virtual element method in two dimensions as a generalised gradient method. This re-formulation allows for computing a reliable and efficient error estimator by locally reconstructing broken fluxes and potentia…
View article: Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system
Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system Open
We derive error estimates of a finite element method for the approximation of solutions to a seven-fields formulation of a magnetohydrodynamics model, which preserves the energy of the system, and the magnetic and cross helicities on the d…
View article: New Crouzeix-Raviart elements of even degree: theoretical aspects, numerical performance, and applications to the Stokes' equations
New Crouzeix-Raviart elements of even degree: theoretical aspects, numerical performance, and applications to the Stokes' equations Open
We construct new Crouzeix-Raviart (CR) spaces of even degree $p$ that are spanned by basis functions mimicking those for the odd degree case. Compared to the standard CR gospel, the present construction allows for the use of nested bases o…
View article: Stability and interpolation estimates of Hellinger-Reissner virtual element spaces
Stability and interpolation estimates of Hellinger-Reissner virtual element spaces Open
We prove stability and interpolation estimates for Hellinger-Reissner virtual elements; the constants appearing in such estimates only depend on the aspect ratio of the polytope under consideration and the degree of accuracy of the scheme.…
View article: A Nečas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuška-Aziz inequality
A Nečas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuška-Aziz inequality Open
View article: A priori and a posteriori error estimates of a $\mathcal C^0$-in-time method for the wave equation in second order formulation
A priori and a posteriori error estimates of a $\mathcal C^0$-in-time method for the wave equation in second order formulation Open
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 order formulation; the resulting method is a Petrov-Galerkin …
View article: A Nečas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuška-Aziz inequality
A Nečas-Lions inequality with symmetric gradients on star-shaped domains based on a first order Babuška-Aziz inequality Open
We prove a Nečas-Lions inequality with symmetric gradients on two and three dimensional domains of diameter $R$ that are star-shaped with respect to a ball of radius $ρ$; the constants in the inequality are explicit with respect to $R$ and…
View article: Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system
Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system Open
We derive error estimates of a finite element method for the approximation of solutions to a seven-fields formulation of a magnetohydrodynamics model, which preserves the energy of the system, and the magnetic and cross helicities on the d…
View article: <i>hp</i>-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes
<i>hp</i>-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes Open
We prove $hp$-optimal error estimates for the original discontinuous Galerkin (DG) method when approximating solutions to first-order hyperbolic problems with constant convection fields in the $L^{2}$ and DG norms. The main theoretical too…
View article: The Nonconforming Virtual Element Method with Curved Edges
The Nonconforming Virtual Element Method with Curved Edges Open
View article: Space-Time Virtual Elements for the Heat Equation
Space-Time Virtual Elements for the Heat Equation Open
We propose and analyze a space-time virtual element method for the discretization of the heat equation in a space-time cylinder, based on a standard Petrov-Galerkin formulation. Local discrete functions are solutions to a heat equation pro…
View article: Enriched virtual elements for plane elasticity with corner singularities
Enriched virtual elements for plane elasticity with corner singularities Open
View article: $hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes
$hp$-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes Open
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 norms. The main theoretical tools used in the analysis are nove…
View article: The role of stabilization in the virtual element method: A survey
The role of stabilization in the virtual element method: A survey Open
The virtual element method was introduced 10 years ago, and has generated a large number of theoretical results and applications ever since. Here, we overview the main mathematical results concerning the stabilization of the method as an i…
View article: Design and performance of a space–time virtual element method for the heat equation on prismatic meshes
Design and performance of a space–time virtual element method for the heat equation on prismatic meshes Open
View article: Design and performance of a space-time virtual element method for the heat equation on prismatic meshes
Design and performance of a space-time virtual element method for the heat equation on prismatic meshes Open
We present a space-time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategies to handle efficiently the space-time mesh structure are d…
View article: $$hp$$-Optimal Interior Penalty Discontinuous Galerkin Methods for the Biharmonic Problem
$$hp$$-Optimal Interior Penalty Discontinuous Galerkin Methods for the Biharmonic Problem Open
View article: The nonconforming virtual element method with curved edges
The nonconforming virtual element method with curved edges Open
We introduce a nonconforming virtual element method for the Poisson equation on domains with curved boundary and internal interfaces. We prove arbitrary order optimal convergence in the energy and $L^2$ norms, and validate the theoretical …
View article: Stability and interpolation properties of serendipity nodal virtual elements
Stability and interpolation properties of serendipity nodal virtual elements Open
We discuss stability and interpolation properties of serendipity nodal virtual element spaces in two and three dimensions. Notably, we rigorously prove stability bounds for the “dofi-dofi” stabilization and show that the best interpolation…
View article: Stability and Interpolation Properties for Stokes-Like Virtual Element Spaces
Stability and Interpolation Properties for Stokes-Like Virtual Element Spaces Open
View article: The virtual element method for the 3D resistive magnetohydrodynamic model
The virtual element method for the 3D resistive magnetohydrodynamic model Open
We present a four-field virtual element discretization for the time-dependent resistive magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral mes…
View article: Interpolation and stability properties of low-order face and edge virtual element spaces
Interpolation and stability properties of low-order face and edge virtual element spaces Open
We analyse the interpolation properties of two-dimensional and three-dimensional low-order virtual element (VE) face and edge spaces, which generalize Nédélec and Raviart–Thomas polynomials to polygonal-polyhedral meshes. Moreover, we inve…
View article: Space-time virtual elements for the heat equation
Space-time virtual elements for the heat equation Open
We propose and analyze a space-time virtual element method for the discretization of the heat equation in a space-time cylinder, based on a standard Petrov-Galerkin formulation. Local discrete functions are solutions to a heat equation pro…
View article: $hp$-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem
$hp$-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem Open
We prove $hp$-optimal error estimates for interior penalty discontinuous Galerkin methods (IPDG) for the biharmonic problem with homogeneous essential boundary conditions. We consider tensor product-type meshes in two and three dimensions,…
View article: Stability and interpolation properties for Stokes-like virtual element spaces
Stability and interpolation properties for Stokes-like virtual element spaces Open
We prove stability bounds for Stokes-like virtual element spaces in two and three dimensions. Such bounds are also instrumental in deriving optimal interpolation estimates. Furthermore, we develop some numerical tests in order to investiga…
View article: Interpolation and stability estimates for edge and face virtual elements of general order
Interpolation and stability estimates for edge and face virtual elements of general order Open
We develop interpolation error estimates for general order standard and serendipity edge and face virtual elements in two and three dimensions. Contextually, we investigate the stability properties of the associated [Formula: see text] dis…
View article: Mortar Coupling of hp-Discontinuous Galerkin and Boundary Element Methods for the Helmholtz Equation
Mortar Coupling of hp-Discontinuous Galerkin and Boundary Element Methods for the Helmholtz Equation Open