The following regulations apply to non-EU citizens who are permanent residents of EØS/EU or Schengen Area member state and hold a valid residence permit or a residence card
Visa-free entry to Greenland/Faroe Islands and a stay of up to 90 days. The days spent in the Faroe Islands and Greenland will count in the 90 days allowed to spend in the Schengen Area
A valid passport and a valid residence permit or card must be presented upon entry.
The following regulations apply to Non-schengen/EU/EØS Citizens without residence permit or recidence card in Schengen/EU/EØS
The Faroe Islands and Greenland are not part of the Schengen cooperation and not a member of the EU, therefore a visa to Denmark and a Schengen visa does not give access to entry into the Faroe Islands and Greenland.
You must apply for a visa "Valid for Faroe Islands" if you come from a country with a visa requirement.
It is a serious offence to enter the Faroe Islands without a visa "Valid for Faroe Islands".