Springer - The Least-Squares Finite Element Method Book

This comprehensive text provides a detailed introduction to the least-squares finite element method (LSFEM) for the numerical solution of partial differential equations (PDEs). Designed for researchers and students in computational science, the book covers essential theory for first-order systems, with a specific focus on the div-curl and the div-curl-grad system. The content applies LSFEM systematically to permissible boundary conditions for the incompressible Navier-Stokes equations. It also explores how the divergence equations in Maxwell equations function, demonstrating they are not redundant. Furthermore, the text provides methods to derive equivalent second-order versions of both the Navier-Stokes and Maxwell equations. By utilizing LSFEM, users can access a method that is simple, efficient, and robust. This makes it a practical tool for solving a wide range of problems in computational fluid dynamics and electromagnetics. This book serves as a vital resource for anyone working within the Scientific Computation series to improve numerical accuracy and efficiency in complex modeling.