which institution did he complete his education in?
Sheffield Scientific School and Connecticut Academy of Arts and Sciences.
Josiah Willard Gibbs
He remained at Yale as a graduate student at the Sheffield Scientific School. At age 19, soon after his graduation from college, Gibbs was inducted into the Connecticut Academy of Arts and Sciences, a scholarly institution composed primarily of members of the Yale faculty.

who was josiah willard gibbs? An American scientist when was he born? February 11, 1839 which field of science was he involved with? Physics, chemistry, and mathematics.
wiki:19643472
Josiah Willard Gibbs [SEP] Education
Though in later years he used glasses only for reading or other close work, Gibbs's delicate health and imperfect eyesight probably explain why he did not volunteer to fight in the Civil War of 1861–65. He was not conscripted and he remained at Yale for the duration of the war.