Book Development Status

This book is being developed alongside the Fall 2026 offering of ME/BME 736: Advanced Finite Element Methods. The status below indicates how much of each chapter has been developed and reviewed. It will be updated as the book progresses.

For this page, complete means that a chapter has a full working draft suitable for use in the course. Complete chapters may still receive copyediting, additional examples, improved exercises, and revisions needed for consistency with later chapters.

Complete

• Chapter 1: Introduction to the Finite Element Method
• Chapter 2: Mathematical Foundations
• Chapter 3: Partial Differential Equations and Variational Formulations
• Chapter 4: Model Problems in Heat Transfer and Solid Mechanics
• Chapter 5: The Finite Element Method in One Dimension
• Chapter 6: Finite Element Approximation in Multiple Dimensions
• Chapter 7: A Priori Error Estimation and Convergence
• Chapter 8: A Posteriori Error Estimation and Adaptive Finite Elements
• Chapter 9: Nonlinear Finite Element Methods

Yet to be started

The material through a posteriori error estimation and adaptivity has been covered in the course. The following chapters still contain placeholders:

• Chapter 10: Transient Finite Element Methods
• Chapter 11: PDE-Constrained Optimization

Last updated: November 9, 2026.