  We consider magnetic flux penetration in a superconducting film with a
concave corner. Unlike convex corners, where the current flow pattern is easily
constructed from Bean's critical state model, the current flow pattern at a
concave corner is highly nontrivial. To address the problem, we do a numerical
flux creep simulation, where particular attention is paid to efficient handling
of the non-local electrodynamics, characteristic of superconducting films in
the transverse geometry. We find that the current stream lines at the concave
corner are close to circular, but the small deviation from exact circles ensure
that the electric field is finite and continuous. Yet, the electric field is,
as expected, very high at the concave corner. At low fields, the critical state
penetration is deeper from the concave corner than from the straight edges,
which is a consequence of the electrodynamic non-locality. A magneto-optical
experiment on a YBCO displays an almost perfect match with the magnetic flux
distribution from the simulation, hence verifying the necessity of including
electrodynamic non-locality in the modelling of superconducting thin films.
