Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations

2012 John H Barrett Memorial Lectures

Xiaobing Feng, Ohannes Karakashian, Yulong Xing (Herausgeber)

Buch | Softcover

XII, 279 Seiten

2016 | Softcover reprint of the original 1st ed. 2014
Springer International Publishing (Verlag)
978-3-319-37840-4 (ISBN)

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The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.

A quick tutorial on discontinuous Galerkin methods for elliptic problems.- Discontinuous Galerkin methods for time dependent problems: survey and recent developments.- Adaptivity and error estimation for discontinuous Galerkin methods.- $C^0$ interior penalty methods for 4th order problems.- Devising superconvergent discontinuous Galerkin methods.- A local time stepping Runge-Kutta discontinuous Galerkin method for hurricane storm surge modeling.- An overview of the discontinuous Petrov-Galerkin method.- Discontinuous Galerkin methods for radiative transport equations.- Error control for discontinuous Galerkin methods for first order hyperbolic problems.- Virtual elements and discontinuous Galerkin methods.- Time-discrete higher order ALE formulations: a DG approach.- Discontinuous finite element methods for coupled surface-subsurface flow and transport problems .

Erscheinungsdatum	20.08.2016
Reihe/Serie	The IMA Volumes in Mathematics and its Applications
Zusatzinfo	XII, 279 p. 72 illus., 58 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Adaptivity • Analysis • A Priori and a Posteriori Error Estimates • Calculus and mathematical analysis • Differential calculus and equations • discontinuous Galerkin methods • mathematics and statistics • Numerical analysis • Partial differential equations
ISBN-10	3-319-37840-6 / 3319378406
ISBN-13	978-3-319-37840-4 / 9783319378404
Zustand	Neuware