Finite Element Methods and Their Applications (Scientific Computation)

"This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain 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 in each chapter are provided."--Résumé de l'éditeur "This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain 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 in each chapter are provided."--BOOK JACKET 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....Pages 1-85 Nonconforming Finite Elements....Pages 87-116 Mixed Finite Elements....Pages 117-171 Discontinuous Finite Elements....Pages 173-213 Characteristic Finite Elements....Pages 215-259 Adaptive Finite Elements....Pages 261-304 Solid Mechanics....Pages 305-320 Fluid Mechanics....Pages 321-335 Fluid Flow in Porous Media....Pages 337-362 Semiconductor Modeling....Pages 363-384 A numerical approach for solving a differential equation problem is to dis-cretize this problem, which has infinitely many degrees of freedom, to produce a discrete problem, which has finitely many degrees of freedom and can be solved using a computer.