Numerical treatment of partial differential equations / Christian Grossmann, Hans-Görg Roos ; translated and revised by Martin Stynes.

محفوظ في:
التفاصيل البيبلوغرافية
منشور في: Berlin ; New York : Springer, c2007.
المؤلف الرئيسي:
Grossmann, Christian
مؤلفون آخرون:
Roos, Hans-Görg, 1949-
Stynes, M. (Martin), 1951-
سلاسل:Universitext
الموضوعات:
Differential equations, Partial > Numerical solutions.
Finite differences.
Finite element method.
Numerical analysis.
التنسيق: كتاب
Numerical treatment of partial differential equations /
جدول المحتويات:
  • 1. Basics
  • 1.1. Classification and Correctness
  • 1.2. Fourier's Method, Integral Transforms
  • 1.3. Maximum Principle, Fundamental Solution
  • 2. Finite Difference Methods
  • 2.1. Basic Concepts
  • 2.2. Illustrative Examples
  • 2.3. Transportation Problems and Conservation Laws
  • 2.4. Elliptic Boundary Value Problems
  • 2.5. Finite Volume Methods as Finite Difference Schemes
  • 2.6. Parabolic Initial-Boundary Value Problems
  • 2.7. Second-Order Hyperbolic Problems
  • 3. Weak Solutions
  • 3.1. Introduction
  • 3.2. Adapted Function Spaces
  • 3.3. Variational Equations and Conforming Approximation
  • 3.4. Weakening V-ellipticity
  • 3.5. Nonlinear Problems
  • 4. The Finite Element Method
  • 4.1. A First Example
  • 4.2. Finite-Element-Spaces
  • 4.3. Practical Aspects of the Finite Element Method
  • 4.4. Convergence of Conforming Methods
  • 4.5. Nonconforming Finite Element Methods
  • 4.6. Mixed Finite Elements
  • 4.7. Error Estimators and Adaptive FEM
  • 4.8. The Discontinuous Galerkin Method
  • 4.9. Further Aspects of the Finite Element Method
  • 5. Finite Element Methods for Unsteady Problems
  • 5.1. Parabolic Problems
  • 5.2. Second-Order Hyperbolic Problems
  • 6. Singularly Perturbed Boundary Value Problems
  • 6.1. Two-Point Boundary Value Problems
  • 6.2. Parabolic Problems, One-dimensional in Space
  • 6.3. Convection-Diffusion Problems in Several Dimensions
  • 7. Variational Inequalities, Optimal Control
  • 7.1. Analytic Properties
  • 7.2. Discretization of Variational Inequalities
  • 7.3. Penalty Methods
  • 7.4. Optimal Control of PDEs
  • 8. Numerical Methods for Discretized Problems
  • 8.1. Some Particular Properties of the Problems
  • 8.2. Direct Methods
  • 8.3. Classical Iterative Methods
  • 8.4. The Conjugate Gradient Method
  • 8.5. Multigrid Methods
  • 8.6. Domain Decomposition, Parallel Algorithms
  • Bibliography: Textbooks and Monographs
  • Bibliography: Original Papers.

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