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A Virtual Element Method for elastic and inelastic problems on polytope meshes
We present a Virtual Element Method (VEM) for possibly nonlinear elastic and
inelastic problems, mainly focusing on a small deformation regime. The
numerical scheme is based on a low-order approximation of the displacement
field, as well as a suitable treatment of the displacement gradient. The
proposed method allows for general polygonal and polyhedral meshes, it is
efficient in terms of number of applications of the constitutive law, and it
can make use of any standard black-box constitutive law algorithm. Some
theoretical results have been developed for the elastic case. Several numerical
results within the 2D setting are presented, and a brief discussion on the
extension to large deformation problems is included
Serendipity Face and Edge VEM Spaces
We extend the basic idea of Serendipity Virtual Elements from the previous
case (by the same authors) of nodal (-conforming) elements, to a more
general framework. Then we apply the general strategy to the case of
and conforming Virtual Element Methods, in two and three dimensions
Serendipity Nodal VEM spaces
We introduce a new variant of Nodal Virtual Element spaces that mimics the
"Serendipity Finite Element Methods" (whose most popular example is the 8-node
quadrilateral) and allows to reduce (often in a significant way) the number of
internal degrees of freedom. When applied to the faces of a three-dimensional
decomposition, this allows a reduction in the number of face degrees of
freedom: an improvement that cannot be achieved by a simple static
condensation. On triangular and tetrahedral decompositions the new elements
(contrary to the original VEMs) reduce exactly to the classical Lagrange FEM.
On quadrilaterals and hexahedra the new elements are quite similar (and have
the same amount of degrees of freedom) to the Serendipity Finite Elements, but
are much more robust with respect to element distortions. On more general
polytopes the Serendipity VEMs are the natural (and simple) generalization of
the simplicial case
Lowest order Virtual Element approximation of magnetostatic problems
We give here a simplified presentation of the lowest order Serendipity
Virtual Element method, and show its use for the numerical solution of linear
magneto-static problems in three dimensions. The method can be applied to very
general decompositions of the computational domain (as is natural for Virtual
Element Methods) and uses as unknowns the (constant) tangential component of
the magnetic field on each edge, and the vertex values of the
Lagrange multiplier (used to enforce the solenoidality of the magnetic
induction ). In this respect the method can be seen
as the natural generalization of the lowest order Edge Finite Element Method
(the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost
arbitrary shape, and as we show on some numerical examples it exhibits very
good accuracy (for being a lowest order element) and excellent robustness with
respect to distortions
Medición de la actividad fÃsica en la población española mediante cuestionarios: direcciones futuras de investigación
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