This book investigates the theoretical underpinnings and practical applications of least-squares finite element methods (LSFEM) for solving partial differential equations. It is written by Pavel B. Bochev, a recognized expert in the field, and draws upon extensive research and computational experience. The text presents a unified framework for understanding LSFEM, emphasizing their advantages in terms of stability and accuracy compared to traditional methods. It explores various formulations and their suitability for different classes of problems in science and engineering.

The book is recognized as a significant contribution to the literature on finite element methods, particularly for its rigorous treatment of least-squares formulations. It is considered a valuable resource for researchers and graduate students seeking a deep understanding of LSFEM. The text is noted for its thoroughness and the clarity with which complex theoretical concepts are presented, making it a standard reference for those working in computational mathematics and applied sciences.