Log In Sign Up

A serendipity fully discrete div-div complex on polygonal meshes

by   Michele Botti, et al.

In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. The keystone of the reduction process is a new estimate of symmetric tensor-valued polynomial fields in terms of boundary values, completed with suitable projections of internal values for higher degrees. We prove an extensive set of new results for the original complex and show that the reduced complex has the same homological and analytical properties as the original one. This paper also contains an appendix with proofs of general Poincaré–Korn-type inequalities for hybrid fields.


page 1

page 2

page 3

page 4


New degrees of freedom for differential forms on cubical meshes

We consider new degrees of freedom for higher order differential forms o...

An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem

In this work, following the discrete de Rham (DDR) approach, we develop ...

A fully discrete plates complex on polygonal meshes with application to the Kirchhoff-Love problem

In this work we develop a novel fully discrete version of the plates com...

Data assimilation for a quasi-geostrophic model with circulation-preserving stochastic transport noise

This paper contains the latest installment of the authors' project on de...

A conservative, physically compatible discretization for turbidity currents

The recently introduced Mass Energy Enstrophy and Vorticity conserving (...

Complexes from complexes

This paper is concerned with the derivation and properties of differenti...