The Mimetic Discretization (MD) method is an approach for the approximation of PDE problems that shares common features with the finite element and the finite difference schemes. The MD method enjoys the same variational background of finite elements, but focuses the attention on the degrees of freedom rather than the underlying basis functions. This construction allows for MD schemes with general polygonal/polyhedral meshes and, in general, it grants a richer flexibility with respect to FE methods. In the present talk, an MD method for scalar elliptic problems with arbitrary and fully local polynomial degree is investigated. Moreover, the possibility of obtaining arbitrarily regular underlying spaces is also studied.
Mimetic discretizations of arbitrary local order and regularity
L Beirao da Veiga;G Manzini
2011
Abstract
The Mimetic Discretization (MD) method is an approach for the approximation of PDE problems that shares common features with the finite element and the finite difference schemes. The MD method enjoys the same variational background of finite elements, but focuses the attention on the degrees of freedom rather than the underlying basis functions. This construction allows for MD schemes with general polygonal/polyhedral meshes and, in general, it grants a richer flexibility with respect to FE methods. In the present talk, an MD method for scalar elliptic problems with arbitrary and fully local polynomial degree is investigated. Moreover, the possibility of obtaining arbitrarily regular underlying spaces is also studied.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
