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Numerical Analysis Research Group

The numerical analysis group at OSU focuses mainly on the study of numerical methods for partial differential equations. Topics we have been working on include continuous and discontinuous Galerkin methods, the finite volume methods, a priori and a posteriori error estimations, least squares methods, various preconditioning techniques, and numerical implementations. We also have extended interests in other related topics such as finite difference methods, numerical linear algebra, and large-scale computing. Accurate and efficient numerical methods can be used to successfully simulate many complicated physical processes in areas such as solid and fluid mechanics, surface sciences, electromagnetism, and mathematical finance, etc.

Faculty

  • Ning Ju

    Ph.D., Indiana, 1999.

    Applied mathematics.

  • JaEun Ku

    Ph.D., Cornell, 2004.

    Numerical analysis, Finite Element methods for Partial differential equations, Least-Squares Methods for Linear Elasticity problems and Navier-Stokes equations, A posteriori error estimates

  • Eduardo Teixeira

    Dr. Teixeira’s research explores how structure and order emerge from nonlinear and often singular phenomena governed by partial differential equations. His work combines rigorous analysis with geometric insight, drawing on ideas from PDE theory, geometric measure theory, and applied mathematics. A central focus is the fine regularity of solutions and their interfaces—key to interpreting complex models. Ultimately, his research seeks to uncover the principles through which complexity organizes into patterns, illuminating fundamental mechanisms in mathematical and physical systems.

  • Xu Zhang

    B.S./M.S., Sichuan University; Ph.D., Virginia Tech, 2013.

    Dr. Zhang's research is on numerical analysis and scientific computing. In particular, he is interested in numerical methods for partial differential equations. Recently, his research focuses on immersed finite element methods for interface problems including algorithm development, implementation, error analysis, and engineering applications.

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