Nonlinear PDE's, Numerical Analysis, and Applications; October 2-3, 2015; Pittsburgh, PA

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

Conference: Nonlinear PDEs, Numerical Analysis, and Applications, October 2-3, 2015, University of Pittsburgh. Partial differential equations (PDEs) play a key role in the understanding, simulation and prediction of various phenomena occurring in the sciences and engineering. Yet even for simple problems, exact mathematical solutions are unattainable, and computational methods are necessary to construct approximate solutions. Therefore there is a critical need to develop numerical methods and to theoretically justify the quality and reliability of the resulting approximations. In addition to providing justification of the numerical methods, the theoretical analysis often gives insight for the development of new methods with improved efficiency, accuracy and capabilities. This two-day conference will create a forum for junior and senior researchers to discuss cutting-edge results and applications of numerical methods for nonlinear PDEs. The aim of the conference is to provide an informal setting in which young researchers and leading experts in numerical analysis can meet, collaborate, and develop new ideas. In addition, the conference will expose graduate students and postdocs on this active field of numerical PDEs. The construction, implementation, and analysis of computational methods for fully nonlinear second order partial differential equations are relatively new, yet critical research areas in numerical analysis and scientific computing. Such problems arise in many application areas including meteorology, cosmology, geometric optics, differential geometry, optimal transport, economics, imagine processing and mesh generation. These problems constitute one of the most difficult classes of PDEs to approximate numerically, and breakthroughs in their discretization have only appeared within the last 15 years. While there have been several advances in numerical fully nonlinear second order PDEs, there still remain fundamental challenges that need to be properly addressed. Examples include the construction of nonlinear Galerkin methods with monotonicity properties under realistic mesh conditions, robust numerical methods for general families of nonlinear problems, imposition of non-standard boundary conditions, and fast solvers of the resulting non-linear algebraic systems. This conference will gather leaders in the field to discuss state-of-the-art research trends and directions of future research.