In a classical concert setting, how could you describe how a violin compliments a piano in a duo?

Answer 1

The violin is not playing an accompaniment to the piano, like another writer said. On the contrary, if you're talking about violin/piano sonatas, which is what this would be, for the most part, in the case of Mozart, the piano is accompanying the violin. In the case of Beethoven sonatas, however, the two instruments have an equal role (Beethoven was a pianist and was, well, Beethoven...)

If you're talking about solo repertoire for violin that has a piano accompaniment, written, based on the orchestral score then again, the piano is accompanying the violin, not the other way around.

Answer 2

The violin is playing the accompaniment, and it plays a counter-melody compared to the piano, which is playing the harmony and melody.