A Simple Introduction to the Mixed Finite Element Method

1. Front Matter

   Pages i-xii

   PDF

2. Introduction

   • Gabriel N. Gatica

   Pages 1-25

3. Babuška–Brezzi Theory

   • Gabriel N. Gatica

   Pages 27-60

4. Raviart-Thomas Spaces

   • Gabriel N. Gatica

   Pages 61-91

5. Mixed Finite Element Methods

   • Gabriel N. Gatica

   Pages 93-126

6. Back Matter

   Pages 127-132

   PDF

The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.

• Babuska-Brezzi's theory
• Dual-mixed formulations
• Raviart-Thomas spaces
• boundary value problems in continuum mechanics
• inf-sup conditions
• partial differential equations

From the book reviews:

“This monograph provides a nicely focused and mathematically rigorous introduction to the mixed finite element method. … This monograph should be very useful to Ph.D. students and researchers eager to obtain a firm grasp on the mathematical analysis of mixed finite element methods for the Poisson and linear elasticity equations, and constitutes a solid starting point from which to explore further the rich literature on the subject.” (Alexandre Ern, Mathematical Reviews, January, 2015)

• Centro de Investigaciòn en Ingenierìa Matemàtica and Departamento de Ingenierìa Matemàtica, Universidad de Concepciòn, Concepciòn, Chile

  Gabriel N. Gatica

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