Explore the words cloud of the CAVE project. It provides you a very rough idea of what is the project "CAVE" about.
The following table provides information about the project.
UNIVERSITA' DEGLI STUDI DI MILANO-BICOCCA
|Coordinator Country||Italy [IT]|
|Total cost||980˙634 €|
|EC max contribution||980˙634 € (100%)|
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
|Duration (year-month-day)||from 2016-07-01 to 2021-06-30|
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|1||UNIVERSITA' DEGLI STUDI DI MILANO-BICOCCA||IT (MILANO)||coordinator||980˙634.00|
The Virtual Element Method (VEM) is a novel technology for the discretization of partial differential equations (PDEs), that shares the same variational background as the Finite Element Method. First but not only, the VEM responds to the strongly increasing interest in using general polyhedral and polygonal meshes in the approximation of PDEs without the limit of using tetrahedral or hexahedral grids. By avoiding the explicit integration of the shape functions that span the discrete space and introducing an innovative construction of the stiffness matrixes, the VEM acquires very interesting properties and advantages with respect to more standard Galerkin methods, yet still keeping the same coding complexity. For instance, the VEM easily allows for polygonal/polyhedral meshes (even non-conforming) with non-convex elements and possibly with curved faces; it allows for discrete spaces of arbitrary C^k regularity on unstructured meshes. The main scope of the project is to address the recent theoretical challenges posed by VEM and to assess whether this promising technology can achieve a breakthrough in applications. First, the theoretical and computational foundations of VEM will be made stronger. A deeper theoretical insight, supported by a wider numerical experience on benchmark problems, will be developed to gain a better understanding of the method's potentials and set the foundations for more applicative purposes. Second, we will focus our attention on two tough and up-to-date problems of practical interest: large deformation elasticity (where VEM can yield a dramatically more efficient handling of material inclusions, meshing of the domain and grid adaptivity, plus a much stronger robustness with respect to large grid distortions) and the cardiac bidomain model (where VEM can lead to a more accurate domain approximation through MRI data, a flexible refinement/de-refinement procedure along the propagation front, to an exact satisfaction of conservation laws).
|year||authors and title||journal||last update|
L. Beirao da Veiga, G. Manzini, L. Mascotto
A posteriori error estimation and adaptivity in hp virtual elements
published pages: , ISSN: 0945-3245, DOI: 10.1007/s00211-019-01054-6
L. BeirÃ£o da Veiga, A. Chernov, L. Mascotto, A. Russo
Exponential convergence of the hp virtual element method in presence of corner singularities
published pages: 581â€“613, ISSN: 0029-599X, DOI: 10.1007/s00211-017-0921-7
|Numerische Mathematik 138||2019-10-15|
L. BeirÃ£o da Veiga, F. Dassi, A. Russo
High-order Virtual Element Method on polyhedral meshes
published pages: 1110-1122, ISSN: 0898-1221, DOI: 10.1016/j.camwa.2017.03.021
|Computers & Mathematics with Applications 74/5||2019-10-15|
L. BeirÃ£oÂ daÂ Veiga, F. Brezzi, F. Dassi, L.D. Marini, A. Russo
Virtual Element approximation of 2D magnetostatic problems
published pages: 173-195, ISSN: 0045-7825, DOI: 10.1016/j.cma.2017.08.013
|Computer Methods in Applied Mechanics and Engineering 327||2019-10-15|
LourenÃ§o BeirÃ£o da Veiga, Carlo Lovadina, Alessandro Russo
Stability analysis for the virtual element method
published pages: 2557-2594, ISSN: 0218-2025, DOI: 10.1142/S021820251750052X
|Mathematical Models and Methods in Applied Sciences 27/13||2019-10-15|
LourenÃ§o BeirÃ£o da Veiga, Alessandro Russo, Giuseppe Vacca
The Virtual Element Method with curved edges
published pages: , ISSN: 0764-583X, DOI: 10.1051/m2an/2018052
|ESAIM: Mathematical Modelling and Numerical Analysis||2019-10-15|
L. BeirÃ£o da Veiga, F. Brezzi, F. Dassi, L.D. Marini, A. Russo
Lowest order Virtual Element approximation of magnetostatic problems
published pages: 343-362, ISSN: 0045-7825, DOI: 10.1016/j.cma.2017.12.028
|Computer Methods in Applied Mechanics and Engineering 332||2019-10-15|
L. BeiraÍ‚o da Veiga, C. Lovadina, G. Vacca
Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes
published pages: 1210-1242, ISSN: 0036-1429, DOI: 10.1137/17m1132811
|SIAM Journal on Numerical Analysis 56/3||2019-10-15|
LourenÃ§o BeirÃ£o da Veiga, Franco Brezzi, L. Donatella Marini, Alessandro Russo
Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems
published pages: 399-416, ISSN: 2426-8399, DOI: 10.5802/smai-jcm.40
|SMAI Journal of Computational Mathematics 4||2019-10-15|
H. Chi, L. BeirÃ£o da Veiga, G.H. Paulino
Some basic formulations of the virtual element method (VEM) for finite deformations
published pages: 148-192, ISSN: 0045-7825, DOI: 10.1016/j.cma.2016.12.020
|Computer Methods in Applied Mechanics and Engineering 318||2019-10-15|
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