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Pre-Publicación 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.

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