Bernardo Cockburn

Bernardo Cockburn is a Distinguished McKnight University Professor in the School of Mathematics at the University of Minnesota. He has been a faculty member since 1987, progressing from Assistant Professor to Associate Professor in 1992, and achieving full Professor status in 1997. He also held positions as an Affiliate Professor at the University of Delaware (2019-2020) and Chair Professor of Mathematics at King Fahd University of Petroleum and Minerals in Saudi Arabia (2012-2014).

• Education: Ph.D. from University of Chicago (1986), Doctorat de 3eme Cycle from University of Paris VI/INRIA (1983), Masters and Licenciatura from Universidad Nacional de Ingenieria in Lima, Peru
• Research Focus: Numerical methods for partial differential equations, particularly discontinuous Galerkin methods

Cockburn's research primarily centers on the devising and analysis of efficient methods for numerically solving linear and nonlinear partial differential equations. His most significant contribution has been in the development and analysis of discontinuous Galerkin methods, particularly the hybridizable discontinuous Galerkin (HDG) methods which he pioneered. His work spans error estimation for hyperbolic problems, continuous dependence for Hamilton-Jacobi equations, and numerous applications across fluid dynamics, structural mechanics, and electromagnetics. He has developed theoretical frameworks for superconvergence properties and created practical algorithms for a wide range of engineering applications.

Analysis of his recent publications reveals a strong focus on hybridizable discontinuous Galerkin methods, with significant contributions to superconvergence theory, error estimation, and applications to diverse physical problems including Stokes flow, linear elasticity, Timoshenko beams, and convection-diffusion problems. His work demonstrates a clear trajectory from theoretical foundations to practical implementation, with increasing emphasis on curved domains, adaptive methods, and coupling techniques between different numerical approaches.

• Doctor Honoris Causa from Universidad Nacional de Ingenieria, Lima, Peru (2013)
• Invited Speaker at the International Congress of Mathematicians, Numerical Analysis Section (2010)
• Distinguished McKnight University Professor, University of Minnesota (2007)

Cockburn has supervised an impressive 23 PhD students throughout his career, many of whom have gone on to become professors at major universities worldwide including the University of Puerto Rico, Purdue University, and University of Concepcion in Chile. His advisees have produced significant research in discontinuous Galerkin methods, particularly in applications to structural mechanics, fluid dynamics, and Hamilton-Jacobi equations. His research has been supported by numerous grants from the National Science Foundation and other funding agencies, enabling extensive collaboration with researchers across the United States and internationally.

Cockburn leads a vibrant research group focused on computational mathematics, with particular emphasis on developing and analyzing discontinuous Galerkin methods. His work has fostered significant collaboration between mathematicians and engineers, with applications spanning aerospace, civil engineering, and materials science. The research group maintains strong connections with institutions worldwide, including regular collaborations with researchers in Peru, Chile, and Europe, reflecting Cockburn's international background and influence.