Discontinuous Galerkin Methods For Solving Elliptic And Parabolic Equations

by Riviere, Beatrice

• ISBN13: 9780898716566
• ISBN10: 089871656X
• Format: Paperback
• Copyright: 2008-07-31
• Publisher: Society for Industrial & Applied

Summary

Discontinous Galerkin (DG) methods for solving partial differential equations, developed in the late 1990s, have become popular among computational scientists. Covering both theory and computation, this book focuses on three primal DG methods - the symmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and nonsymmetric interior penalty Galerkin - which are variations of interior penalty methods. The author provides the basic tools for analysis and discusses coding issues, including data structure, construction of local matrices, and assembling of the global matrix. Computational examples and applications to important engineering problems are also included. Part I focuses on the application of DG methods to second order elliptic problems in one dimension and in higher dimensions. Part II presents the time-dependent parabolic problems - with and without convection. Part III contains applications of DG methods to solid mechanics (linear elasticity), fluid dynamics (Stokes and NavierStokes), and porous media ow (two-phase and miscible displacement).

Author Biography

Beatrice Riviere is an Associate Professor in the Department of Computational and Applied Mathematics at Rice University.

Table of Contents

List of figures

List of tables

List of algorithms

Preface

Elliptic Problems

One-dimensional problem

Higher dimensional problem

Parabolic Problems

Purely parabolic problems

Parabolic problems with convection

Applications

Linear elasticity

Stokes flow

Navier-Stokes flow

Flow in porous media

Quadrature rules

DG codes

An approximation result

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.