Luisa Donatella Marini
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Luisa Donatella Marini has a total of 51 co-authors. Here are the top co-authors by number of shared publications:
- Franco Brezzi
IMATI - CNR, Via A. Ferrata 5/A, 27100 Pavia, Italy
49 shared publications - Alessandro Russo
Dipartimento di Matematica e Applicazioni, Universita degli Studi di Milano-Bicocca, Milano, Italy
21 shared publications - Lourenco Beirao da Veiga
Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca Via Roberto Cozzi 55 -20125 Milano Italy
18 shared publications - Franco Dassi
University of Milano-Bicocca
6 shared publications - Paola Pietra
Istituto di Analisi Numerica del C.N.R.
6 shared publications - Douglas N. Arnold
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
3 shared publications
Latest Publications
- 10 January 2026
- Published by World Scientific Pub Co Pte Ltd in Mathematical Models and Methods in Applied Sciences
- Vol. 36 (03) , 601-628
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 [ ], optimal convergence rates. Whenever the exact solution is a polynomial of degree [ ], local spaces of degree [ ] 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.
- 10 January 2026
- Published by World Scientific Pub Co Pte Ltd in Mathematical Models and Methods in Applied Sciences
- Vol. 36 (03) , 601-628
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 [ ], optimal convergence rates. Whenever the exact solution is a polynomial of degree [ ], local spaces of degree [ ] 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.
- 2 January 2026
- Published by World Scientific Pub Co Pte Ltd in Mathematical Models and Methods in Applied Sciences
- Vol. 36 (02) , 235-241
Essays and reviews on new trends in kinetic theory, active particles, and hyperbolic systems toward scientific machine learning
This editorial paper introduces the articles published in a special issue focused on essays and reviews, which offer a forward-looking perspectives on new frontiers of applied mathematics. First, a brief description of the scientific contributions of the papers published in this issue is provided. Then, based on the papers’ contents, a forward look at research perspectives is brought to the reader’s attention. These perspectives focus on new developments of the kinetic theory of classical and active particles, behavioral swarms, and numerical and analytical study of hyperbolic systems. Finally, our editorial explores how the contents of this issue can have an impact on mathematical tools of Scientific Machine learning Applied to the study of collective dynamics of living systems.
- 2 January 2026
- Published by World Scientific Pub Co Pte Ltd in Mathematical Models and Methods in Applied Sciences
- Vol. 36 (02) , 235-241
Essays and reviews on new trends in kinetic theory, active particles, and hyperbolic systems toward scientific machine learning
This editorial paper introduces the articles published in a special issue focused on essays and reviews, which offer a forward-looking perspectives on new frontiers of applied mathematics. First, a brief description of the scientific contributions of the papers published in this issue is provided. Then, based on the papers’ contents, a forward look at research perspectives is brought to the reader’s attention. These perspectives focus on new developments of the kinetic theory of classical and active particles, behavioral swarms, and numerical and analytical study of hyperbolic systems. Finally, our editorial explores how the contents of this issue can have an impact on mathematical tools of Scientific Machine learning Applied to the study of collective dynamics of living systems.
- Open Access
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.Open AccessA 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. - Top Cited PapersOpen Access
- 11 May 2023
- Published by Cambridge University Press (CUP) in Acta Numerica
- Vol. 32, 123-202
The virtual element method
The present review paper has several objectives. Its primary aim is to give an idea of the general features of virtual element methods (VEMs), which were introduced about a decade ago in the field of numerical methods for partial differential equations, in order to allow decompositions of the computational domain into polygons or polyhedra of a very general shape.Nonetheless, the paper is also addressed to readers who have already heard (and possibly read) about VEMs and are interested in gaining more precise information, in particular concerning their application in specific subfields such as ${C}^1$ -approximations of plate bending problems or approximations to problems in solid and fluid mechanics.- 11 May 2023
- Published by Cambridge University Press (CUP) in Acta Numerica
- Vol. 32, 123-202
Top Cited PapersOpen AccessThe virtual element method
The present review paper has several objectives. Its primary aim is to give an idea of the general features of virtual element methods (VEMs), which were introduced about a decade ago in the field of numerical methods for partial differential equations, in order to allow decompositions of the computational domain into polygons or polyhedra of a very general shape.Nonetheless, the paper is also addressed to readers who have already heard (and possibly read) about VEMs and are interested in gaining more precise information, in particular concerning their application in specific subfields such as ${C}^1$ -approximations of plate bending problems or approximations to problems in solid and fluid mechanics. - 3 March 2021
- Published by Springer Nature in Vietnam Journal of Mathematics
- Vol. 49 (3) , 871-899
Finite Elements and Virtual Elements on Classical Meshes
- 3 March 2021
- Published by Springer Nature in Vietnam Journal of Mathematics
- Vol. 49 (3) , 871-899
Finite Elements and Virtual Elements on Classical Meshes
- Open Access
Virtual Elements and curved edges
We present a new method to construct Virtual Element spaces on polygons with curved edges.
Open AccessVirtual Elements and curved edges
We present a new method to construct Virtual Element spaces on polygons with curved edges.
- Open Access
A family of three-dimensional virtual elements with applications to magnetostatic
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 doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming ($0$-forms), $H({\rm {\bf curl}})$-conforming ($1$-forms), and $H({\rm div})$-conforming ($2$-forms) functional spaces in three dimensions, and they would surely be useful for other problems and in more general contexts.Open AccessA family of three-dimensional virtual elements with applications to magnetostatic
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 doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming ($0$-forms), $H({\rm {\bf curl}})$-conforming ($1$-forms), and $H({\rm div})$-conforming ($2$-forms) functional spaces in three dimensions, and they would surely be useful for other problems and in more general contexts. - Open Access
- 1 April 2018
- Published by Elsevier in Computer Methods in Applied Mechanics and Engineering
- Vol. 332, 343-362
Lowest order Virtual Element approximation of magnetostatic problems
- 1 April 2018
- Published by Elsevier in Computer Methods in Applied Mechanics and Engineering
- Vol. 332, 343-362
Open AccessLowest order Virtual Element approximation of magnetostatic problems
- 2 February 2018
- Published by Springer Nature in Chinese Annals of Mathematics, Series B
- Vol. 39 (2) , 315-334
Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions
- 2 February 2018
- Published by Springer Nature in Chinese Annals of Mathematics, Series B
- Vol. 39 (2) , 315-334
Serendipity Virtual Elements for General Elliptic Equations in Three Dimensions
- 1 January 2018
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 56 (5) , 2940-2962
A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics
We consider, as a simple model problem, the application of virtual element methods (VEMs) to the linear magnetostatic three-dimensional problem in the formulation of Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming (0-forms), $H(curl)$-conforming (1-forms), and $H(div)$-conforming (2-forms) functional spaces in three dimensions, and they could surely be useful for other problems and in more general contexts.
- 1 January 2018
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 56 (5) , 2940-2962
A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics
We consider, as a simple model problem, the application of virtual element methods (VEMs) to the linear magnetostatic three-dimensional problem in the formulation of Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming (0-forms), $H(curl)$-conforming (1-forms), and $H(div)$-conforming (2-forms) functional spaces in three dimensions, and they could surely be useful for other problems and in more general contexts.