This book provides a comprehensive, self-contained guide to solutions of partial differential equations with both finite element and finite volume methods. Upon discussing different formulations of finite element methods, it focuses on solution techniques with various formulations, including collocation, Galerkin, least squares, and stabilized finite element methods. In turn, it presents solutions to problems concerning heat transfer, coupled heat and mass transfer, and structures applications. The book also covers problems relating to incompressible and compressible flow, magnetic refrigeration, and aerodynamics of high-speed reentry vehicles. All in all, this book is intended to equip graduate students and researchers with enough implementation details for using finite element and finite volume methods in a variety of applications in both structural mechanics and fluid dynamics.

Dr. Rakesh Ranjan earned his Ph.D. from the Department of Mechanical Engineering at Texas A&M University in 2010. He worked with Dr. J N Reddy during his Doctoral studies at the Advanced Computational Mechanics Laboratory. His work at Texas A&M involved solving structures problems with high order methods. Subsequently he worked as a Postdoctoral Fellow at the Department of Mechanical Engineering at the University of Texas, San Antonio (UTSA) from 2010-2013. At UTSA he augmented the SUPG and GLS stabilized finite element formulations for incompressible flow. Some of his contributions also involved solving hyperelastic deformations with applications in stress induced tissue growth. He subsequently joined Los Alamos National Laboratory (LANL) as a Research Associate in the Nuclear Engineering and Non-Proliferation Division (NEN) in 2013. He implemented a projection method to replace the convolution approach for solving incompressible free surface flow at LANL. Subsequently, he joined Astronautics Corporation of America at the Madison Center as a Senior Computational Modeler in 2015. Later he worked as a Senior Research Associate with the Department of Aerospace and Mechanical Engineering at the University of Oklahoma in 2017. His work at the University of Oklahoma involved solving compressible flow problems with non-equilibrium aero-thermodynamics considerations with applications in hypersonic atmospheric re-entry flow. He is currently with the University of Dayton, Research Institute and Air Force Research Laboratory (WPAFB) as an Aerothemodynamic Research Engineer, and concurrently as a Research Scientist with the Department of Mechanical Engineering, University of Texas, San Antonio (UTSA).