Recent results and perspectives for virtual element methods

2021 ◽  
pp. 1-6
Author(s):  
L. Beirao da Veiga ◽  
N. Bellomo ◽  
F. Brezzi ◽  
L. D. Marini
Keyword(s):  
Critical Analysis ◽  
Special Issue ◽  
Research Perspectives ◽  
Virtual Element Methods ◽  
Virtual Element

This editorial paper is devoted to present the papers published in a special issue focused on recent views, applications, and results of virtual element methods (VEM). A critical analysis of the overall contents of the issue is proposed, thus leading to a forward look to research perspectives.

Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems

2021 ◽  
pp. 1-7
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
M. A. J. Chaplain
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Mathematical Models ◽  
Modeling And Simulation ◽  
Critical Analysis ◽  
Living Systems ◽  
Special Issue ◽  
Research Perspectives ◽  
Heterogeneous Features

This editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous features of the complex system under consideration. Subsequently, the contents of the papers in this issue are presented referring to the aforementioned complexity features. Finally, a critical analysis of the overall contents of the issue is proposed, with the aim of providing a forward look to research perspectives.

Active particles methods and challenges in behavioral systems

2020 ◽  
Vol 30 (04) ◽  
pp. 653-658 ◽  
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
J. Soler
Keyword(s):  
Qualitative Analysis ◽  
Critical Analysis ◽  
Mathematical Approach ◽  
Special Issue ◽  
Behavioral Systems ◽  
Research Perspectives ◽  
Active Particles ◽  
Challenging Research ◽  
Large Systems

This paper first provides an introduction to the mathematical approach to the modeling, qualitative analysis, and simulation of large systems of living entities, specifically self-propelled particles. Subsequently, a presentation of the papers published in this special issue follows. Finally, a critical analysis of the overall contents of the issue is proposed, thus leading to define some challenging research perspectives.

Collective dynamics in science and society

2021 ◽  
pp. 1-6
Author(s):  
N. Bellomo ◽  
F. Brezzi
Keyword(s):  
Critical Analysis ◽  
Large Scale ◽  
Particle Methods ◽  
Science And Society ◽  
Special Issue ◽  
Collective Dynamics ◽  
Multiscale Problems ◽  
Research Perspectives ◽  
Active Particles ◽  
Large Systems

This editorial paper presents the articles published in a special issue devoted to active particle methods applied to modeling, qualitative analysis, and simulation of the collective dynamics of large systems of interacting living entities in science and society. The modeling approach refers to the mathematical tools of behavioral swarms theory and to the kinetic theory of active particles. Applications focus on classical problems of swarms theory, on crowd dynamics related to virus contagion problems, and to multiscale problems related to the derivation of models at a large scale from the mathematical description at the microscopic scale. A critical analysis of the overall contents of the issue is proposed, with the aim to provide a forward look to research perspectives.

Recent results and challenges in behavioral systems

2020 ◽  
Vol 30 (10) ◽  
pp. 1857-1862 ◽  
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
J. Soler
Keyword(s):  
Qualitative Analysis ◽  
Critical Analysis ◽  
Special Issue ◽  
Collective Dynamics ◽  
Behavioral Systems ◽  
Research Perspectives

This editorial paper is devoted to present the papers published in a special issue focused on modeling, qualitative analysis and simulation of the collective dynamics of living, self-propelled particles. A critical analysis of the overall contents of the issue is proposed, thus leading to a forward look to research perspectives.

Recent techniques for PDE discretizations on polyhedral meshes

2014 ◽  
Vol 24 (08) ◽  
pp. 1453-1455 ◽  
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
G. Manzini
Keyword(s):  
Discontinuous Galerkin ◽  
Finite Differences ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Special Issue ◽  
Polyhedral Meshes ◽  
Recent Developments ◽  
Virtual Element Methods ◽  
Mimetic Finite Differences ◽  
Virtual Element

This brief paper is an introduction to the papers published in a special issue devoted to survey on recent techniques for discretizing Partial Differential Equations on general polygonal and polyhedral meshes. The number of different techniques to deal with discretizations on polygonal and polyhedral meshes is quite huge, and their history is quite long. Here we concentrate on the most recent techniques, including Mimetic Finite Differences, Virtual Element Methods, and the recent developments, in this direction, of Finite Volumes and Discontinuous Galerkin Methods.

Touchy-Feely History: The ‘Stuff’ of American Culture

2015 ◽  
Vol 4 (1) ◽  
pp. 4-18
Author(s):  
Lauren Rebecca Sklaroff
Keyword(s):  
Material Culture ◽  
Cultural History ◽  
Race And Ethnicity ◽  
The Body ◽  
Special Issue ◽  
Historical Significance ◽  
Research Perspectives ◽  
Economic Trends ◽  
Recent Trends ◽  
New Research

This state of the field essay examines recent trends in American Cultural History, focusing on music, race and ethnicity, material culture, and the body. Expanding on key themes in articles featured in the special issue of Cultural History, the essay draws linkages to other important literatures. The essay argues for more a more serious consideration of the products within popular culture, less as a reflection of social or economic trends, rather for their own historical significance. While the essay examines some classic texts, more emphasis is on work published within the last decade. Here, interdisciplinary methods are stressed, as are new research perspectives developing by non-western historians.

scholarly journals Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients

2021 ◽  
Author(s):  
Andreas Dedner ◽  
Alice Hodson
Keyword(s):  
Fourth Order ◽  
Perturbation Parameter ◽  
Two Dimensions ◽  
Optimal Error Estimates ◽  
Projection Operators ◽  
Varying Coefficients ◽  
Virtual Element Methods ◽  
Virtual Element ◽  
Perturbation Problems ◽  
Fourth Order Problems

Abstract We present a class of nonconforming virtual element methods for general fourth-order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element spaces. Optimal error estimates in the energy norm are provided for general linear fourth-order problems with varying coefficients. We also discuss fourth-order perturbation problems and present a novel nonconforming scheme which is uniformly convergent with respect to the perturbation parameter without requiring an enlargement of the space. Numerical tests are carried out to verify the theoretical results. We conclude with a brief discussion on how our approach can easily be applied to nonlinear fourth-order problems.

Some Estimates for Virtual Element Methods

2017 ◽  
Vol 17 (4) ◽  
pp. 553-574 ◽  
Author(s):  
Susanne C. Brenner ◽  
Qingguang Guan ◽  
Li-Yeng Sung
Keyword(s):  
Error Estimates ◽  
Three Dimensions ◽  
Poisson Problem ◽  
Polyhedral Meshes ◽  
Virtual Element Methods ◽  
Virtual Element

AbstractWe present novel techniques for obtaining the basic estimates of virtual element methods in terms of the shape regularity of polygonal/polyhedral meshes. We also derive new error estimates for the Poisson problem in two and three dimensions.

scholarly journals Towards developing multimodal literacies in the ESP classroom: methodological insights and practical applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Belinda Crawford Camiciottoli ◽  
Inmaculada Fortanet-Gómez
Keyword(s):  
English For Specific Purposes ◽  
Knowledge Dissemination ◽  
Multimodal Approach ◽  
Special Issue ◽  
Multimodal Literacy ◽  
Research And Practice ◽  
Practical Applications ◽  
Innovative Research ◽  
Research Perspectives ◽  
Literacy Research

Abstract In this article, we provide an introduction to this special issue of Multimodal Communication entitled “Multimodal approaches in ESP: Innovative research and practice”. The Special Issue showcases innovative research presented at the 2019 International Conference on Knowledge Dissemination and Multimodal Literacy: Research Perspectives on ESP in a Digital Age. After briefly discussing the multimodal approach in language teaching and specifically in English for Specific Purposes (ESP) and its key role in developing multimodal competence, each of the five featured contributions is previewed. The contributions offer theoretically grounded and research-informed applications of the multimodal approach in the ESP classroom.

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