Elliptic Differential Equations Theory and Numerical Treatment /

• Main Author: Hackbusch, Wolfgang (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2017.
• Edition: 2nd ed. 2017.
• Series: Springer Series in Computational Mathematics, 18
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; System theory.; Numerical analysis.; Calculus of variations.; Physics.; Analysis.; Numerical Analysis.; Systems Theory, Control.; Calculus of Variations and Optimal Control; Optimization.; Theoretical, Mathematical and Computational Physics.

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before ad...

Table of Contents:

• 1 Partial Differential Equations and Their Classification Into Types
• 2 The Potential Equation
• 3 The Poisson Equation
• 4 Difference Methods for the Poisson Equation
• 5 General Boundary Value Problems
• 6 Tools from Functional Analysis
• 7 Variational Formulation
• 8 The Method of Finite Elements
• 9 Regularity
• 10 Special Differential Equations
• 11 Eigenvalue Problems
• 12 Stokes Equations.