This book investigates the mathematical underpinnings of the Finite Element Method (FEM). It provides a rigorous analysis of the theoretical foundations and numerical aspects crucial for the effective application of FEM in various scientific and engineering disciplines. The text focuses on the mathematical formulation, error analysis, and convergence properties of different finite element schemes, aiming to equip readers with a deep understanding of the method's behavior and limitations.

The book is likely to be regarded as a comprehensive and mathematically rigorous treatment of the Finite Element Method, suitable for advanced students and researchers in applied mathematics, engineering, and related fields. Its focus on theoretical aspects suggests it serves as a foundational text for understanding the method's behavior rather than a practical guide to software implementation. The depth of mathematical analysis indicates it is intended for readers with a strong background in calculus, linear algebra, and differential equations.