STABILITY OF THE STOKES PROJECTION ON WEIGHTED SPACES AND APPLICATIONS

A. J. SALGADO; E. OTÁROLA; R. G. DURÁN

MATHEMATICS OF COMPUTATION

AMER MATHEMATICAL SOC

Lugar: Providence; Año: 2020 vol. 89 p. 1581 - 1603

0025-5718

We show that, on convex polytopes and two or three dimensions, the finite element Stokes projection is stable on weighted spaces $\bW^{1,p}_0(\omega,\Omega) \times L^p(\omega,\Omega)$, where the weight belongs to a certain Muckenhoupt class and the integrability index can be different from two. We show how this estimate can be applied to obtain error estimates for approximations of the solution to the Stokes problem with singular sources.