UID:
almahu_9949199530002882
Format:
XVI, 418 p.
,
online resource.
Edition:
1st ed. 1998.
ISBN:
9783662037409
Series Statement:
Scientific Computation,
Content:
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.
Note:
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.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783642083679
Additional Edition:
Printed edition: ISBN 9783540639343
Additional Edition:
Printed edition: ISBN 9783662037416
Language:
English
DOI:
10.1007/978-3-662-03740-9
URL:
https://doi.org/10.1007/978-3-662-03740-9
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