The phrase our today's meeting is commonly used in Indian English, even though other dialects of English frown upon it. The mentioned examples in the comments of our today's specials and our today's speaker will, I think, sound off to many speakers, but possibly not as much as our today's meeting. Why is "our today's meeting" wrong?

Understanding the Context

- English Language & Usage Stack ... The phrases " on tomorrow," " on today," and " on yesterday " are commonly heard in the southern region of the United States. They are acceptable in casual speech and other informal contexts, but should not be used in formal contexts such as academic writing. american english - Origins and history of "on tomorrow", "on today ...

Key Insights

Neither are clauses, but "today in the afternoon" is grammatical (adverbial phrase of time), while "today afternoon" is not. I would also suggest "this afternoon" as a more succinct and idiomatic alternative to "today in the afternoon". word choice - 'Today afternoon' vs 'Today in the afternoon'? - English ... I think it is a good question.

Final Thoughts

When there is yesterday morning and tomorrow morning, why have an exception for this morning (which means today's morning)? Yes, idiom, but I actually do like idiomatic extensions like these - as long as everybody knows what is meant and no grammar or semantic rules are violated... In old books, people often use the spelling "to-day" instead of "today". When did the change happen? Also, when people wrote "to-day", did they feel, when pronouncing the word, that it contained two