62 citations · 100 across the 8 of their papers we have counts for
8 papers
Virtual Elements on polyhedra with a curved face
Franco Brezzi, L. Donatella Marini
We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons…
A family of three-dimensional virtual elements with applications to magnetostatic
L. Beirão da Veiga, F. Brezzi, F. Dassi +2
We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In…
Serendipity Virtual Elements on Polyhedral Meshes
Lourenco Beirao da Veiga, Franco Brezzi, Franco Dassi +2
We numerically validate the Virtual Element Method of order k for general second order elliptic problems with variable coefficients in three dimensions. Moreover, we investigate nu…
Lowest order Virtual Element approximation of magnetostatic problems
L. Beirão da Veiga, F. Brezzi, F. Dassi +2
We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in thre…
Serendipity Face and Edge VEM Spaces
L. Beirao da Veiga, F. Brezzi, L. D. Marini +1
We extend the basic idea of Serendipity Virtual Elements from the previous case (by the same authors) of nodal (-conforming) elements, to a more general framework. Then we app…
Virtual Element Method for fourth order problems: estimates
Claudia Chinosi, L. Donatella Marini
We analyse the family of -Virtual Elements introduced in \cite{Brezzi:Marini:plates} for fourth-order problems and prove optimal estimates in and in via classical…
Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes
L. Beirao da Veiga, F. Brezzi, L. D. Marini +1
In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable…
A simple preconditioner for a discontinuous Galerkin method for the Stokes problem
Blanca Ayuso de Dios, Franco Brezzi, L. Donatella Marini +2
In this paper we construct Discontinuous Galerkin approximations of the Stokes problem where the velocity field is H(div)-conforming. This implies that the velocity solution is div…