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The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics - Hardcover
Synopsis
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.
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From the Back Cover
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.
Synopsis
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.
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