I will stick my neck out and say:
No, this type of abbreviation does not occur in English, because it reflects a manner of formation of (especially) abstract nouns that is common in German but uncommon in or absent from English.
In this specific example the prefix is the same in both cases, but most important it is — ‘ver’ — which in this context does not change the meaning of the root — tauschen, exchange and schmelzen, melt. It is an inherent linguistic feature of the formation of this kind of verb and often adds emphasis or extends the verbin some way (see Appendix, below). Regardless, it is therefore quite natural for a German speaker to ignore this in forming an abbreviation. In English no prefix directly equivalent to this sense of ‘ver’ exists (again, see Appendix). Prefixes serve to alter or qualify the verb. So in a simple mathematical context we might have opposites, increase and decrease, which could be abbreviated by their first letters and certainly not by removing the prefix.
Consider possible English nouns with different prefixes beginning with the same letter. Often removing the prefix gives a word of different meaning with an unintuitive initial letter — displacement function and devolution function, to snatch something out of the air. P and V? I think not. We’d go for something different entirely. Greek perhaps. Again the difference relates to the language.
My final remark is perhaps irrelevant to the question, but the only example I can think of using an internal letter for an abbreviation is K in the CYMK colour model: Cyan, Yellow, Magenta and BlacK. Here K rather than B is used for black as B stands for Blue in the alternative RBG — Red, Green, Blue — model.
Appendix: Linguistic Expansion
The prefix ‘ver’ can have other meanings in German. The Wiktionary entry list three types 1. As in vergeben (to forgive), which is not further explained but is clearly not of the type under discussion, 2. “denotes a transition of the object into a state, which is indicated by the stem”. Examples include verlieben (to fall in love), which derives from the simple libeben (to love). This is similar to the instances in the question and is very common, and 3. “indicating a faulty action” as in verzahlen (to miscount) from the root zahlen (to count).
I do not think Germans would abbreviate examples of type 3 to the initial letter of the root, which is very different from the complete word.
The English words with a prefix related to the ‘ver’ have the prefix ‘for’ and are all of types 1 or 3, e.g. forgive, forget, forswear. We clearly would not abbreviate them in terms of the root.
The only English prefix that I can think of that serves a similar function to type 2 ‘ver’ is the unrelated ‘en-’, although here the root can also be a noun or adjective, e.g. enact, encase, encircle, encrypt. (The English ‘en-’ may have other meanings in certain words.) It is possible that if there were such things as ‘enactment’ functions and ‘encircling’ functions one might abbreviate them as A and C, maintaining a logical connection. I do not know of an examples in practice.