Discontinuous Galerkin methods for viscous incompressible flow

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This work covers essential topics in numerical analysis and computational methods, focusing on superconvergent techniques. It begins with foundational concepts, including meshes and shape functions, followed by spaces and approximation. The text delves into linear diffusion problems, exploring two distinct sections dedicated to this topic. Subsequent chapters address the Stokes equations and various flow problems, such as the advection-diffusion-reaction equation, Oseen equations, and Navier-Stokes equations. The discussion then shifts to linear solvers, featuring Krylov space methods, interior penalty methods, and local multigrid techniques. It also examines the LDG method and its application to advection-diffusion problems, as well as the Stokes and Oseen equations. Additionally, the book includes example problems that illustrate the application of these methods, covering topics like meshes and domains, the Poisson equation, and the previously mentioned flow equations. Accompanying figures provide visual representations of key concepts, such as eigenvalues on square meshes and the accuracy of various methods. The content is structured to facilitate understanding of complex numerical techniques, making it a valuable resource for those interested in computational fluid dynamics and related fields.