Ivo M. Babuška (born March 22, 1926 in Prague) is a Czech-American mathematician, noted for his studies of the finite element method and the proof of the Babuška–Lax–Milgram theorem in partial differential equations. One of the celebrated result in the finite elements is the so-called Ladyženskaja–Babuška–Brezzi (LBB) condition (also referred to in some literature as Banach–Necas–Babuška (BNB)), which provides sufficient conditions for a stable mixed formulation. The LBB condition has guided mathematicians and engineers to develop state-of-the-art formulations for many technologically important problems like Darcy flow, Stokes flow, incompressible Navier–Stokes, nearly incompressible elasticity. He is also well known for his work on adaptive methods and the p- and hp-versions of the finite element method. He also developed the mathematical framework for the partition of unity methods.
He studied civil engineering at the Czech Technical University in Prague, where he received the Dipl. Ing in 1949. In 1951 he received the degree Dr. Tech.; his doctoral dissertation was supervised by Eduard Čech and Vladimir Knichal. From 1949 he studied at Mathematical Institute of the Czechoslovak Academy of Sciences and then was the head of the Department of Partial Differential Equations. In 1955, he received a Ph.D. in mathematics and in 1960 D.Sc. in mathematics.
Babuška works in the field of mathematics, applied mathematics, numerical methods, finite element methods, and computational mechanics. In 1968, he became a professor at University of Maryland, College Park in the mathematics department, which is part of the University of Maryland College of Computer, Mathematical, and Natural Sciences. He retired in 1996 as a Distinguished University Professor. In 1989 he co-founded the company ESRD, Inc. which developed the StressCheck finite element software, putting into practice much of Babuška's research and contributions to the finite element method. After his time at the University of Maryland, he moved to the Institute for Computational Engineering and Sciences at the University of Texas at Austin where he currently holds the Robert B. Trull Chair in Engineering.
Babuška has published more than 300 papers in refereed journals, more than 70 papers in conference proceedings, and several books. He is an invited speaker at major international conferences and is a member numerous editorial boards for scientific journals. He has received many honors for his work, including four doctorates honoris causa, the Czechoslovak State prize for Mathematics, the Leroy P. Steele Prize (2012), the Birkhoff Prize (1994), the Humboldt Award of Federal Republic of Germany, Honorary Foreign Member of the Czech Learned Society and the Bolzano Medal. In 2003, asteroid 36060 Babuška was named in his honor by the International Astronomical Union. In 2005, Babuska was awarded the Honorary Medal "De Scientia Et Humanitate Optime Meritis" and he was elected to the National Academy of Engineering. He is also a member of the Academy of Medicine, Engineering, and Sciences of Texas.