scholarly journals An arbitrary order Mixed Virtual Element formulation for coupled multi-dimensional flow problems

2022 ◽  
Vol 391 ◽  
pp. 114204
Author(s):  
M.F. Benedetto ◽  
A. Borio ◽  
F. Kyburg ◽  
J. Mollica ◽  
S. Scialò
Keyword(s):  
Arbitrary Order ◽  
Element Formulation ◽  
Flow Problems ◽  
Dimensional Flow ◽  
Virtual Element

scholarly journals Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces

CALCOLO ◽  
2021 ◽  
Vol 58 (3) ◽  
Author(s):  
Elena Bachini ◽  
Gianmarco Manzini ◽  
Mario Putti
Keyword(s):  
Arbitrary Order ◽  
Surface Geometry ◽  
Virtual Element Method ◽  
Anisotropic Character ◽  
Local Reference System ◽  
Local Reference ◽  
Local Parametrization ◽  
Manufactured Solution ◽  
Virtual Element ◽  
Element Method

AbstractWe develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covariant form using an appropriate local reference system. The knowledge of the local parametrization allows us to consider the two-dimensional VEM scheme, without any explicit approximation of the surface geometry. The theoretical properties of the classical VEM are extended to our framework by taking into consideration the highly anisotropic character of the final discretization. These properties are extensively tested on triangular and polygonal meshes using a manufactured solution. The limitations of the scheme are verified as functions of the regularity of the surface and its approximation.

scholarly journals Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics

2021 ◽  
Vol 383 ◽  
pp. 113917
Author(s):  
Andrea Borio ◽  
François P. Hamon ◽  
Nicola Castelletto ◽  
Joshua A. White ◽  
Randolph R. Settgast
Keyword(s):  
Finite Difference ◽  
Element Formulation ◽  
Virtual Element

scholarly journals Virtual element formulation for isotropic damage

2018 ◽  
Vol 144 ◽  
pp. 38-48 ◽  
Author(s):  
Maria Laura De Bellis ◽  
Peter Wriggers ◽  
Blaž Hudobivnik ◽  
Giorgio Zavarise
Keyword(s):  
Element Formulation ◽  
Isotropic Damage ◽  
Virtual Element
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