- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
Discontinuous Galerkin (DG) methods for solving partial differential equations, developed in the late 1990s, have become popular among computational scientists. This book covers both theory and computation as it 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.
Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equation is divided into three parts: 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—without and with convection. Part III contains applications of DG methods to solid mechanics (linear elasticity), ?uid dynamics (Stokes and Navier-Stokes), and porous media ?ow (two-phase and miscible displacement).
Appendices contain proofs and MATLAB® code for one-dimensional problems for elliptic equations and routines written in C that correspond to algorithms for the implementation of DG methods in two or three dimensions.
Contents
List of Figures
List of Tables
List of Algorithms
Preface
Part I: Elliptic Problems
Chapter 1: One-dimensional problem
Chapter 2: Higher dimensional problem
Part II: Parabolic Problems
Chaper 3: Purely parabolic problems
Chapter 4: Parabolic problems with convection
Part III: Applications
Chapter 5: Linear elasticity
Chapter 6: Stokes flow
Chapter 7: Navier-Stokes flow
Chapter 8: Flow in porous media
Appendix A: Quadrature rules
Appendix B: DG codes
Appendix C: An approximation result
Bibliography
Index.
