arXiv subjects

L. Donatella Marini

Publications and source records attributed to L. Donatella Marini.

4 recordsLinked to original sources

arXiv2025

A Virtual Element Method on polyhedra with curved faces

In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann non-homogeneous boundary conditions, and provides, for degree of accuracy $k \geq 1$, optimal convergence rates. Whenever the exact solution is a polynomial of degree $k$, local spaces of degree $k$ ensure satisfaction of the patch test. The proposed method is theoretically analyzed in the two-dimensional case, whereas it is numerically validated both in two and three dimensions.

math.NA↗

arXiv2023

Virtual Elements on polyhedra with a curved face

We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper we introduce a couple of new ideas for the construction of VEM-approximations on domains with curved boundary, both in two and three dimensions. The new approach looks promising, although sound numerical tests should be made to validate the efficiency of the method.

math.NA↗

arXiv2016

Virtual Element Method for fourth order problems: $L^2-$estimates

We analyse the family of $C^1$-Virtual Elements introduced in \cite{Brezzi:Marini:plates} for fourth-order problems and prove optimal estimates in $L^2$ and in $H^1$ via classical duality arguments.

math.NA↗

arXiv2013

A simple preconditioner for a discontinuous Galerkin method for the Stokes problem

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 divergence-free in the whole domain. This property can be exploited to design a simple and effective preconditioner for the final linear system.

math.NA↗