Discontinuous Galerkin methods for solving elliptic and parabolic equations: theory and implementation

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 variationsof interior penalty methods. The author provides the basic tools for analysisand 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 Navier-Stokes), and porous media ?ow (two-phase and miscible displacement). Presents both theory and implementation, with detailed proofs and MATLAB(r) codes provided in the appendices. Intended for numerical analysts, computational and applied mathematicians, and engineers. Also appropriate for a graduate or seniorundergraduate course. Includes important applications for engineers from a variety of fields INDICE: List of figures; List of tables; List of algorithms; Preface; PartI. Elliptic Problems: 1. One-dimensional problem; 2. Higher dimensional problem; Part II. Parabolic Problems: 3. Purely parabolic problems; 4. Parabolic problems with convection; Part III. Applications: 5. Linear elasticity; 6. Stokes flow; 7. Navier-Stokes flow; 8. Flow in porous media; Appendix A. Quadraturerules; Appendix B. DG codes; Appendix C. An approximation result; Bibliography; Index

• ISBN: 978-0-89871-656-6
• Editorial: SIAM
• Encuadernacion: Rústica
• Páginas: 210
• Fecha Publicación: 18/12/2008
• Nº Volúmenes: 1
• Idioma: Inglés