however vs notwithstanding

however and notwithstanding both are adverbs.

Word	Noun	Adjective	Verb	Adverb
however	No	No	No	Yes
notwithstanding	No	No	No	Yes

As adverbs, however and notwithstanding are synonyms defined as:

however and notwithstanding: despite anything to the contrary (usually preceding a concession)

Other synonyms of however include all the same, at the same time, even so, nevertheless, nonetheless, still, withal, yet.

however (adverb)	notwithstanding (adverb)
despite anything to the contrary (usually preceding a concession)	despite anything to the contrary (usually preceding a concession)
in whatever way or manner
to whatever degree or extent
by contrast; on the other hand