The Least-Squares Finite Element Method
Subtitle: Theory and Applications in Computational Fluid Dynamics and Electromagnetics
By: by Bo-nan Jiang
Series: Scientific Computation; Scientific Computation
Publisher: Springer Berlin Heidelberg
Published: 1998
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 418
ISBN-13: 9783642083679; 9783662037409
Subjects: Mathematical optimization; Physics; Computer science
Description: 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.
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Table of contents: title: Contents (preliminary): I. The Basic Concept of the LSFEM; title: 1. Introduction; title: 2. The first-order Scalar Differential Equation in One-Dimension; title: 3. The First-Order System in One-Dimension; title: II. Fundamentals of the LSFEM; title: 4. Fundamentals of the LSFEM; title: 5. The Div-Curl System; title: 6. The Div-Curl-Grad System; title: III. The LSFEM in Fluid Dynamics; title: 7. Inviscid Irrotational Flows; title: 8. Incompressible Viscous Flows; title: 9. Convective Transport; title: 10. Rotational Inviscid Flows; title: 11. Two-face Flows; title: 12. Compressible Viscous Flows; title: 13. High-Speed Compressible Flows; title: 14. P-Version Least-Squares Finite Element Method; title: IV. The LSFEM in Electromagnetics; title: 15. Electromagnetics; title: V. Solution of the Discrete Equations 16. Iterative Methods for Solving Linear Systems of Equations; title: Appendix A: Operation on Vectors; title: B. Green's Formula; title: C. Finite Element Interpolation; title: D. The Lax-Milgram Theory; title: References; title: Index.