Rognes was a student in applied mathematics at the University of Oslo, earning a master's degree in 2005 and completing a Ph.D. in 2009.[1] Her dissertation, Mixed finite element methods with applications to viscoelasticity and gels, was jointly supervised by Ragnar Winther and Hans Petter Langtangen.[2]
After postdoctoral research at the University of Minnesota and the Simula Research Laboratory, she joined the University of Oslo as a lecturer in 2012, and in the same year became a senior researcher for Simula Research. She remained affiliated on a part-time basis with the University of Oslo until 2016, when she became a chief research scientist for Simula Research.[1]