Springer - The Least-Squares Finite Element Method Textbook

Explore a comprehensive introduction to the least-squares finite element method (LSFEM) for the numerical solution of PDEs. This scientific computation text provides a deep dive into the theory for first-order systems, with a specific focus on the div-curl and the div-curl-grad system. This book demonstrates how LSFEM is applied systematically to permissible boundary conditions for the incompressible Navier-Stokes equations. It also explains why the divergence equations in the Maxwell equations are not redundant and provides the derivation for equivalent second-order versions of both the Navier-Stokes and Maxwell equations. Designed for researchers and students in computational fluid dynamics and electromagnetics, LSFEM offers a simple, efficient, and robust approach to solving a wide range of problems. Whether you are studying complex fluid motion or electromagnetic fields, this Springer publication serves as a foundational resource for mastering advanced numerical methods.