|
" The Least-Squares Finite Element Method : "
by Bo-nan Jiang.
| Document Type
|
:
|
BL
|
| Record Number
|
:
|
759354
|
| Doc. No
|
:
|
b579325
|
| Main Entry
|
:
|
by Bo-nan Jiang.
|
| Title & Author
|
:
|
The Least-Squares Finite Element Method : : Theory and Applications in Computational Fluid Dynamics and Electromagnetics\ by Bo-nan Jiang.
|
| Publication Statement
|
:
|
Berlin, Heidelberg : Springer Berlin Heidelberg, 1998
|
| Series Statement
|
:
|
Scientific computation.
|
| Page. NO
|
:
|
(xvi, 418 pages)
|
| ISBN
|
:
|
3662037408
|
|
|
:
|
: 9783662037409
|
| Contents
|
:
|
Contents (preliminary): I. The Basic Concept of the LSFEM --; 1. Introduction --; 2. The first-order Scalar Differential Equation in One-Dimension --; 3. The First-Order System in One-Dimension --; II. Fundamentals of the LSFEM --; 4. Fundamentals of the LSFEM --; 5. The Div-Curl System --; 6. The Div-Curl-Grad System --; III. The LSFEM in Fluid Dynamics --; 7. Inviscid Irrotational Flows --; 8. Incompressible Viscous Flows --; 9. Convective Transport --; 10. Rotational Inviscid Flows --; 11. Two-face Flows --; 12. Compressible Viscous Flows --; 13. High-Speed Compressible Flows --; 14. P-Version Least-Squares Finite Element Method --; IV. The LSFEM in Electromagnetics --; 15. Electromagnetics --; V. Solution of the Discrete Equations 16. Iterative Methods for Solving Linear Systems of Equations --; Appendix A: Operation on Vectors --; B. Green's Formula --; C. Finite Element Interpolation --; D. The Lax-Milgram Theory --; References --; Index.
|
| Abstract
|
:
|
This is the first book devoted to the least-squares finite element method (LSFEM), which is a simple, efficient and robust technique for the numerical solution of partial differential equations. The book demonstrates that the LSFEM can solve a broad range of problems in fluid dynamics and electromagnetics with only one mathematical/computational formulation. The book shows that commonly adopted special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal-order elements, operator splitting and preconditioning, edge elements, vector potential, and so on, are unnecessary. This book introduces the basic theory of the least-squares method for first-order PDE systems, particularly the div-curl system and the div-curl-grad system. It is applied to the study of permissible boundary conditions for the incompressible Navier--Stokes equations, to show that the divergence equations in the Maxwell equations are not redundant, and to derive equivalent second-order versions of the Navier--Stokes equations and the Maxwell equations. This book covers diverse applications such as incompressible viscous flows, rotational inviscid flows, low- or high-Mach-number compressible flows, two-fluid flows, convective flows, and scattering waves.
|
| Subject
|
:
|
Computer science.
|
| Subject
|
:
|
Mathematical optimization.
|
| Subject
|
:
|
Physics.
|
| LC Classification
|
:
|
QC151.B936 1998
|
| Added Entry
|
:
|
Bo-nan Jiang
|
| |