The Least-Squares Finite Element Method

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Sprache: Englisch

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Beschreibung

Here is a comprehensive introduction to the least-squares finite element method (LSFEM) for numerical solution of PDEs. It covers the theory for first-order systems, particularly the div-curl and the div-curl-grad system. Then LSFEM is applied systematically to 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. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics, including incompressible viscous flows, rotational inviscid flows, low-Mach-number compressible flows, two-fluid and convective flows, scattering waves, etc.

Zusammenfassung

This is the first monograph on the LSFEM method

It treats Navier-Stokes and Maxwell equations in one and the same book

Inhaltsverzeichnis

I. Basic Concepts of LSFEM.- 1. Introduction.- 2. First-Order Scalar Equation in One Dimension.- 3. First-Order System in One Dimension.- II. Fundamentals of LSFEM.- 4. Basis of LSFEM.- 5. Div-Curl System.- 6. Div-Curl-Grad System.- III. LSFEM in Fluid Dynamics.- 7. Inviscid Irrotational Flows.- 8. Incompressible Viscous Flows.- 9. Convective Transport.- 10. Incompressible Inviscid Rotational Flows.- 11. Low-Speed Compressible Viscous Flows.- 12. Two-Fluid Flows.- 13. High-Speed Compressible Flows.- IV. LSFEM in Electromagnetics.- 14. Electromagnetics.- V. Solution of Discrete Equations.- 15. The Element-by-Element Conjugate Gradient Method.- Appendices.- A. Operations on Vectors.- B. Green's Formula.- C. Poincaré Inequality.- D. Lax-Milgram Theorem.- References.

Details

Erscheinungsjahr:	1998
Fachbereich:	Astronomie
Genre:	Mathematik , Medizin , Naturwissenschaften , Physik , Technik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Buch
Reihe:	Scientific Computation
Inhalt:	xvi 418 S.
ISBN-13:	9783540639343
ISBN-10:	3540639349
Sprache:	Englisch
Einband:	Gebunden
Autor:	Jiang, Bo-Nan
Hersteller:	Springer Scientific Computation
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 29 mm
Von/Mit:	Bo-Nan Jiang
Erscheinungsdatum:	22.06.1998
Gewicht:	0,771 kg