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

Descripción:

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. . . . . N° de ref. del artículo V9783540639343

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Sinopsis:

De la contraportada: 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.