A note on stable Helmholtz decompositions in 3D. Issue 7 (18th May 2020) - Gatica, Gabriel N.
ABSTRACT: The stability of Helmholtz decompositions in 3D is known to hold for convex Lipschitz-continuous polyhedral regions and for arbitrary (not necessarily convex) domains of class C 1, 1 . In this note we extend this result to non-convex Lipschitz-continuous 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. In addition, the relation with very similar results already available in the literature is also discussed. Finally, some implications of our results on the associated discrete Helmholtz decomposition and its application to the derivation of a posteriori error estimates, are briefly described.