Scientific Computation

Theory and Applications in Computational Fluid Dynamics and Electromagnetics

By: Bo-nan Jiang

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Hardcover | 22 June 1998

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440 Pages

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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.

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Basic Concepts of LSFEM
Introduction	p. 3
First-Order Scalar Equation in One Dimension	p. 11
First-Order System in One Dimension	p. 31
Fundamentals of LSFEM
Basis of LSFEM	p. 47
Div-Curl System	p. 81
Div-Curl-Grad System	p. 97
LSFEM in Fluid Dynamics
Inviscid Irrotational Flows	p. 115
Incompressible Viscous Flows	p. 129
Convective Transport	p. 201
Incompressible Inviscid Rotational Flows	p. 241
Low-Speed Compressible Viscous Flows	p. 259
Two-Fluid Flows	p. 285
High-Speed Compressible Flows	p. 303
LSFEM in Electromagnetics
Electromagnetics	p. 331
Solution of Discrete Equations
The Element-by-Element Conjugate Gradient Method	p. 385
Operations on Vectors	p. 397
Green's Formula	p. 397
Poincare Inequality	p. 398
Lax-Milgram Theorem	p. 398
References	p. 399
Index	p. 413
Table of Contents provided by Blackwell. All Rights Reserved.

Scientific Computation

Theory and Applications in Computational Fluid Dynamics and Electromagnetics

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Hardcover

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