Asadzadeh M. An Introduction to the Finite Element Method for Differential Equations

Hoboken (NJ): John Wiley & Sons, 2020. — 334 p. — ISBN: 1119671647.The objective of this book is two-fold. The first objective is to construct, as much as possible, stable finite element schemes without affecting accuracy. The second objective is to derive convergence of the numerical schemes up to maximal available regularity of the exact solution. The first two chapters of the book cover existence, uniqueness and stability as well as the working environment, such as vector and function spaces and principle mathematical inequalities. Chapters 3 and 4 cover the approximation procedure with piecewise linears, interpolation, numerical integration and numerical solution of linear system of equations. Chapters 5 through 7 are devoted to the finite element approximations for the one-space dimensional, boundary value problems, initial value problems, and initial-boundary value problems. Finally, Chapters 8 through 10 are an extension of Chapters 3 and 5-7 to higher spatial dimensions. This book is a great resource for upper undergraduates and graduates in applied math, engineering and natural sciences, as well as researchers in industry and academia in need of finite element approximation techniques.True PDF