عنوان

The Least-Squares Finite Element Method :

(Number (ISBN

3662037408

(Number (ISBN

9783662037409

Number

b579325

Title Proper

The Least-Squares Finite Element Method :

General Material Designation

[Book]

Other Title Information

Theory and Applications in Computational Fluid Dynamics and Electromagnetics

First Statement of Responsibility

by Bo-nan Jiang.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1998

Specific Material Designation and Extent of Item

(xvi, 418 pages)

Series Title

Scientific computation.

Text of Note

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.

Text of Note

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.

Computer science.

Mathematical optimization.

Physics.

Class number

Book number

by Bo-nan Jiang.

Bo-nan Jiang

Electronic name

[Book]

Y