The Least-Squares Finite Element Method
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-2228-4 (ISBN)
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This work presents a comprehensive introduction to the least-squares finite element method (LSFEM) as a unified method for the numerical solution of partial differential equations in engineering and physics. In this book a reasonably rigorous mathematical framework of the LSFEM is established without specialized mathematical knowledge beyond calculus and elementary differential equations. The book makes a thorough study of the div-curl system and the div-curl-grad system, then uses this new knowledge to analyze the incompressible Navier-Stokes equations and to derive their non-standard boundary conditions. Anyone who solves partial differential equations by numerical methods, whether he is an engineer, a mathematician or a scientist, should find this book of interest.
Part 1 The basic concept of the least-squares finite element method: the first-order scalar differential equations in one dimension; the first-order system in one dimension. Part 2 Fundamentals of the least-squares finite element method: fundamentals of the least-squares method; the div-curl system; the div-curl-grad system. Part 3 The least-squares finite element method in fluid dynamics: inviscid flows; incompressible viscous flows; compressible viscous flows; convective transport; high-speed compressible flows; p-version least-squares finite element method. Part 4 The least-squares finite element method in electromagnetics: electromagnetics. Part 5 Solution of the discrete equations: iterative methods for solving linear systems of equations. Appendices: operation on vectors; Green's formula; finite element interpolation.
| Zusatzinfo | references, index |
|---|---|
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik | |
| Technik ► Nachrichtentechnik | |
| ISBN-10 | 981-02-2228-9 / 9810222289 |
| ISBN-13 | 978-981-02-2228-4 / 9789810222284 |
| Zustand | Neuware |
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