In 2011, Fonseca was elected president of the Society for Industrial and Applied Mathematics,[3] serving in office from 2013 to 2014.[5] She also served on the Mathematical Sciences jury for the Infosys Prize in 2014 and 2015. Furthermore, she is currently serving as the Chair of SIAM's Activity Group on Mathematical Aspects of Materials Science, with the term lasting until December 31, 2024.[6]
In addition, Fonseca was elected to serve as a Vice President of the American Mathematical Society for a three-year term, beginning in February 2024.[7]
Fonseca is a knight of the Order of Saint James of the Sword.[3]
In 2009, Fonseca was elected as a fellow of SIAM "for contributions to nonlinear partial differential equations and the calculus of variations".[10] In 2012 she became a fellow of the American Mathematical Society.[11] She is also a former AMS Council member at large.[12] In 2021, she was elected to the European Academy of Sciences (EURASC) [13] and, in 2022, she received the Senior Prize from the International Society for the Interaction of Mechanics and Mathematics for "her outstanding contributions to the calculus of variations and the mathematics of materials science, along with her exemplary service to the mathematical community and for being an inspirational mentor and role model for female mathematicians."[14]