The Stokes Complex for Virtual Elements with Application to Navier-Stokes Flows

Beirão da Veiga L.; Mora D.; Vacca G.

Abstract

In the present paper, we investigate the underlying Stokes complex structure of the Virtual Element Method for Stokes and Navier-Stokes introduced in previous papers by the same authors, restricting our attention to the two dimensional case. We introduce a Virtual Element space Phi(h) subset of H-2(Omega) and prove that the triad {Phi(h), V-h, Q(h)} (with V-h and Q(h) denoting the discrete velocity and pressure spaces) is an exact Stokes complex. Furthermore, we show the computability of the associated differential operators in terms of the adopted degrees of freedom and explore also a different discretization of the convective trilinear form. The theoretical findings are supported by numerical tests.

Más información

Título según WOS: The Stokes Complex for Virtual Elements with Application to Navier-Stokes Flows
Título según SCOPUS: The Stokes Complex for Virtual Elements with Application to Navier–Stokes Flows
Título de la Revista: JOURNAL OF SCIENTIFIC COMPUTING
Volumen: 81
Número: 2
Editorial: SPRINGER/PLENUM PUBLISHERS
Fecha de publicación: 2019
Página de inicio: 990
Página final: 1018
Idioma: English
DOI:

10.1007/s10915-019-01049-3

Notas: ISI, SCOPUS