It depends on the meaning of "immersed interface methods." If it is to be considered a a whole, a single thing, then singular is correct, if it represents many different methods consider individually, then the subject should be plural.
Let me give you an example that might help clarify. I live in the USA. I might say:
a popular country is the United States.
"States" is technically plural, so this doesn't seem to fit, but "United States" is considered idiomatically a single entity.
To give another example:
On the football squad, a popular topic of conversation is girls.
Again "girls" is plural, but it is considered just one thing for the subject of this sentence.
So for you, you have two options:
A popular approach is the so-called "immersed interface methods."
To emphasize the unified nature of the methods, I have quoted it, which helps a lot in understanding. The qualifier "so-called" adds to this a lot, indicating that it is called that as a common idiomatic construction. Or alternatively:
Popular approaches are the the so-called immersed interface methods.