SITO NON PIU' AGGIORNATO - UNIVERSITÀ DI PAVIA

Dipartimento di Matematica ''F. Casorati''

HomeEvents › A class of mixed finite element methods based on the Helmhol [...]IT|EN

A class of mixed finite element methods based on the Helmholtz decomposition

Mira Schedensack (HU Berlin and Universität Bonn)

Sala conferenze IMATI-CNR - Monday, May 11, 2015 h.15:00


Abstract. The construction of non-conforming finite element methods (FEMs) is motivated by robust discretizations and mass conservation properties in the simulation of solid and fluid mechanics and by low-order ansatz spaces for higher-order problems as the biharmonic problem for the Kirchhoff plate in structural mechanics. A natural generalization to higher polynomial degrees which preserves the inherent properties of the discretizations is not known so far.
This talk generalizes the non-conforming FEMs of Morley and Crouzeix and Raviart by novel mixed formulations for mth-Laplace equations of the form (−1)mmu=f for arbitrary m = 1, 2, 3, . . . These formulations are based on a new Helmholtz decomposition which decomposes an unstructured tensor field into a higher-order derivative and a curl. The new formulations allow for ansatz spaces of arbitrary polynomial degree and its discretizations coincide with the mentioned non-conforming FEMs for the lowest polynomial degree. The discretizations presented in this talk allow not only for a uniform implementation for arbitrary m, but they also allow for lowest-order ansatz spaces, e.g., piecewise affine polynomials for arbitrary m. Besides the a priori and a posteriori analysis, the talk presents optimal convergence rates for adaptive algorithms for the new discretizations.

Scarica allegato

Back to events page


Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602