This distinctive textbook serves as a professional reference for those who want to solve partial differential equations using finite element methods. The author introduces every concept in the simplest possible setting and maintains a level of treatment that is as rigorous as possible, without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references are included in each chapter.

^{Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract.}

Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications.

Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling.

Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.

Elementary Finite Elements.- Nonconforming Finite Elements.- Mixed Finite Elements.- Discontinuous Finite Elements.- Characteristic Finite Elements.- Adaptive Finite Elements.- Solid Mechanics.- Fluid Mechanics.- Fluid Flow in Porous Media.- Semiconductor Modeling.