Abstract:  It is widely believed that high-order accurate numerical methods, for example discontinuous Galerkin (DG) methods, will eventually replace the traditional low-order methods in the solution of many problems, including fluid flow, solid dynamics, and wave propagation. The talk will give an overview of this field, including the theoretical background of the numerical schemes, the efficient implementation of the methods, and examples of real-world applications. Topics include high-order compact and sparse numerical schemes, high-quality unstructured curved mesh generation, scalable preconditioners for parallel iterative solvers, fully discrete adjoint methods for PDE-constrained optimization, and implicit-explicit schemes for the partitioning of coupled fluid-structure interaction problems. The methods will be demonstrated on some important practical problems, including the inverse design of energetically optimal flapping wings and large eddy simulation (LES) of wind turbines. Bio sketch:  Per-Olof Persson is an Associate Professor of Mathematics at the University of California, Berkeley, since July 2008. Before then, he was an Instructor of Applied Mathematics at the Massachusetts Institute of Technology, from where he also received his Ph.D. in 2005. In his Ph.D. thesis, Persson developed the DistMesh algorithm which is now a widely used unstructured meshing technique for implicit geometries and deforming domains. He has also worked for several years with the development of commercial numerical software, in the finite element package COMSOL Multiphysics. His current research interests are in high-order discontinuous Galerkin methods for computational fluid and solid mechanics. He has developed new efficient numerical discretizations, scalable parallel preconditioners and nonlinear solvers, space-time and curved mesh generators, adjoint formulations for optimization, and IMEX schemes for high-order partitioned Multiphysics solvers. He has applied his methods to important real-world problems such as the simulation of turbulent flow problems in flapping flight and vertical axis wind-turbines, quality factor predictions for micromechanical resonators, and noise prediction for aeroacoustics phenomena.