meet with vs run up against

meet with

verb
  • To encounter; to experience. 

  • To contact or touch (something). 

  • To have a meeting with (someone). 

  • To strike (something). 

  • To answer (something) with; to respond to (something) with. 

run up against

verb
  • To begin to encounter problems with (someone or something). 

How often have the words meet with and run up against occurred in a corpus of books? (source: Google Ngram Viewer )