The Least-Squares Finite Element Method. Theory and Applications in Computational Fluid Dynamics and Electromagnetics.

Jiang, Bo-Nan

ISBN 10: 3540639349 / ISBN 13: 9783540639343

Published by Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1998

About this Item

A comprehensive introduction to the least-squares finite element method (LSFEM) for numerical solutions of PDEs. The text covers the theory for first-order systems, particularly the div-curl and the div-curl-grad system second-order versions of the Navier-Stokes equations and the Maxwell equations. Series: Scientific Computation. Num Pages: 434 pages, 11 black & white tables, biography. BIC Classification: PHDF; PHK. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 234 x 156 x 25. Weight in Grams: 791. . 1998. Hardback. . . . .

Seller Inventory # V9783540639343

Bibliographic Details

• Title: The Least-Squares Finite Element Method. Theory and Applications in Computational Fluid Dynamics and Electromagnetics.
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Publication Date: 1998
• Language: English
• ISBN 10: 3540639349
• ISBN 13: 9783540639343
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

From the Back Cover

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.