Is there a basis in Islamic law for saying "Allahu Akbar" when ascending and "Subhan Allah" when descending?

It is recommended to say "Allahu Akbar" (God is the Greatest) when ascending and "Subhanallah" (Glory be to God) when descending, only during travel, because this is what was reported from the Prophet, peace and blessings be upon him. As for ascending stairs or similar in a settled, non-traveling state, that is not legislated, as acts of worship are prescriptive and limited to what is ورد in the Prophetic Sunnah.