This book considers recent developments in very high-order accurate numerical discretization techniques for partial differential equations. Primary attention is given to the equations of computational fluid dynamics with additional consideration given to the Hamilton-Jacobi, Helmholtz, and elasticity equations. This book should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The volume consists of five articles prepared by leading specialists covering the following specific topics: high-order finite volume discretization via essentially non-oscillatory (ENO) and weighted essentially oscillatory (WENO) reconstruction, the discontinuous Galerkin method, the Galerkin least-squares method, spectral and $hp$-finite element methods, and the mortar finite element method. Implementational and efficiency issues associated with each method are discussed throughout the book
CONTENT
High Order Approximations for Compressible Fluid Dynamics on Un structured and Cartesian Meshes -- Discontinuous Galerkin Methods for Convection-Dominated Problems -- Adaptive Spectral Element Methods for Turbulence and Transition -- hp-FEM for Fluid Flow Simulation -- High Order ENO and WENO Schemes for Computational Fluid Dynamics
