Preprint 2016-03
Gabriel N. Gatica:
A note on stable Helmholtz decompositions in 3D
Abstract:
The stability of Helmholtz decompositions in 3D is known to hold for convex polyhedral regions and for arbitrary (not necessarily convex) domains of class $C^{1,1}$. In this note we extend this result to non-convex polyhedral regions and to the case of homogeneous Neumann boundary conditions on a part of the boundary that is contained in the boundary of a convex extension of the original region. Some implications on the associated discrete Helmholtz decomposition and its application to the derivation of a posteriori error estimates, are also discussed.
This preprint gave rise to the following definitive publication(s):
Gabriel N. GATICA: A note on stable Helmholtz decompositions in 3D. Applicable Analysis, vol. 99, 7, pp. 1110-1121, (2020).