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Pre-Publicación 2016-03

Gabriel N. Gatica:

A note on stable Helmholtz decompositions in 3D


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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