He is known for his fundamental contributions in the development of mathematical methods and numerical tools used to solve partial differential equations, including high-resolution and adaptive mesh refinement schemes.

His primary area of research involves the development of high-resolution schemes and adaptive mesh refinement methods for the solution of partial differential equations.

[3] Colella has also been the leader of a project in NASA's Computational Technologies for Earth and Space Sciences, called "Block-Structured Adaptive Mesh Refinement Methods for Multiphase Microgravity Flows and Star Formation".

[1] Colella is a member of the National Academy of Sciences since 2004 and Fellow of Society for Industrial and Applied Mathematics (SIAM).

[4] He is the recipient of many honors, including the Sidney Fernbach Award from the IEEE Computer Society in 1998, given each year to one person who has made "an outstanding contribution in the application of high performance computers using innovative approaches.