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Math Colloquium
Franziska Weber Univ. of Maryland Title: Structure preserving numerical methods for nonlinear partial differential equations modeling complex fluids Abstract: Nonlinear partial differential equations (PDEs) emerge as mathematical descriptions of many phenomena in physics, biology, engineering, and other fields. No unified mathematical theory is available as of now, and showing existence and uniqueness of solutions to nonlinear PDEs is often challenging. Their solutions can develop singularities of various type, such as shock waves, rapid oscillations, and blow-ups. This complex behavior complicates the task of developing numerical methods to approximate nonlinear PDEs. Good numerical methods should be stable and efficient but at the same time capture the true physical behavior and singularities that the solution may display. When designing numerical methods with such desirable properties, it is crucial to mimic properties that the continuous solution of the PDE has - for example, physical constraints or energy balances - at the discrete level. In this talk, we will examine the procedure of constructing numerical methods that preserve the underlying structure of the solution to the PDE at the discrete level and prove that the numerical schemes converge. In particular, we will focus on numerical methods for nonlinear PDEs that arise as simplified models for liquid crystal dynamics and the Rosensweig model for ferrofluids (magnetically conducting particles in a carrier fluid).Date: Friday, December 1, 2017Time: 4:30 pmLocation: Wean Hall 7218Submitted by: BohmanNote: Refreshments at 4:00 pm, Wean Hall 6220. |