Ebook: Finite Element Methods and Their Applications

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.

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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.

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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.
Content:
Front Matter....Pages I-XIII
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
Back Matter....Pages 385-410

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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.
Content:
Front Matter....Pages I-XIII
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
Back Matter....Pages 385-410
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