Franco Brezzi (born 29 April 1945 in Vimercate) is an Italian mathematician.
He received in 1967 his Ph.D. (Laurea) under the supervision of Enrico Magenes from the Università di Pavia. He was a professor ordinarius of mathematical analysis at the Politecnico di Torino from 1976 to 1977 and then from 1977 to 2006 at the Università degli Studi di Pavia. He was a professor of numerical analysis at the Istituto Universitario di Studi Superiori (IUSS) in Pavia from 2006 until his retirement as professor emeritus in 2015.
His research deals with, among other subjects, the theory and applications of the finite element method in structural methods, fluid mechanics, and electrodynamics. Brezzi's best-known result is the independent derivation in 1974 of the Ladyschenskaja-Babuška-Brezzi condition, often called the inf-sup condition. The LBB condition is a sufficient condition for the numerical stability of mixed finite element problems with saddle point structure, such as the discretization of the incompressible Navier-Stokes equations or the treatment of Darcy's law in differential form.
His doctoral students include Annalisa Buffa and Alfio Quarteroni.
Brezzi has served as a managing editor for Mathematical Models & Methods in Applied Sciences, as the editor-in-chief of Calcolo and Numerische Mathematik, and as a member of the editorial staffs of numerous journals.
He is a member of the Accademia dei Lincei, of the European Academy of Sciences and of the Istituto Lombardo. He was elected in 2002 a fellow of the International Association of Computational Mechanics (IACM) and in 2015 a fellow of the Society for Industrial and Applied Mathematics. He is a Highly Cited Researcher of the ISI.
Brezzi was the president of the Unione Matematica Italiana from 2006 to 2012. He was the director of the Istituto di Analisi Numerica of the CNR from 1992 to 2002 and of the Istituto di Matematica Applicata e Tecnologie Informatiche and the director of CNR from 2002 to 2012. Currently he is the vice president of the European Mathematical Society.