The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics (Scientific Computation)

Book Description
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.

Book Info
Demonstrates that the LSFEM can solve a broad range of problems in fluid dynamics & electromagnetics with only one mathematical/computational formulation, & shows that commonly adopted special treatments in computational fluid dynamics & computational electromagnetics are unnecessary.


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