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We present a class of discretisation spaces and H(div)-conformal elements that can be built on any polytope. Bridging the flexibility of the Virtual Element spaces towards the elements shape with the divergence properties of the Raviart-Thomas elements on the boundaries, the designed frameworks offer a wide range of H(div)-conformal discretisations. As those elements are set up through degrees of freedom, their definitions are easily amenable to the properties the approximated quantities are wished to fulfil. Furthermore, we show that one straightforward restriction of this general setting share its properties with the classical Raviart-Thomas elements at each interface, for any order and any polytopial shape. Then, we investigate the shape of the basis functions corresponding to particular elements in the two dimensional case.
Edge (or Nedelec) finite elements are theoretically sound and widely used by the computational electromagnetics community. However, its implementation, specially for high order methods, is not trivial, since it involves many technicalities that are n
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected by the bo
The $H^m$-conforming virtual elements of any degree $k$ on any shape of polytope in $mathbb R^n$ with $m, ngeq1$ and $kgeq m$ are recursively constructed by gluing conforming virtual elements on faces in a universal way. For the lowest degree case $k
An algebraic multilevel iteration method for solving system of linear algebraic equations arising in $H(mathrm{curl})$ and $H(mathrm{div})$ spaces are presented. The algorithm is developed for the discrete problem obtained by using the space of lowes
In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of the schemes is obtained by adding to the mass balance stabilization te