In the past decade, the numerical approximation of partial differential equations (PDEs) has been pushed into new and exciting application areas. Complex phenomena, with fine-scale structure, can be modeled by "generalized", fractional order differential equations. Many types of free boundary problems in science and engineering have a significant geometric component, such as curvature. Liquid crystal (LC) models combine both geometric and topological constraints with vector and tensor order parameters to yield a coarse-grained description of the physics of LC devices. Optimal transport, a major theory in analysis, has now become a practical tool with many applications. And modern adaptive algorithms are able to optimize and balance the computational effort to capture small scales without over-resolving the others.
This conference aims to bring together a diverse set of researchers in numerical analysis to present state-of-the-art algorithms and approximation techniques for the problems listed above. It will provide a collegial atmosphere for productive discussion and interchange of ideas regarding new tools for studying the stability, approximation, and convergence of numerical methods to solve a diverse range of problems in numerical analysis and scientific computing. The conference will also celebrate Ricardo H. Nochetto's 70th birthday, and honor his contributions to all of the above areas.