Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems Theory, Algorithm, and Applications
This book deals with the adaptive numerical solution of parabolic partial differential equations (PDEs) arising in many branches of applications. It illustrates the interlocking of numerical analysis, the design of an algorithm and the solution of practical problems. In particular, a combination of...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2001, 2001
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| Edition: | 1st ed. 2001 |
| Series: | Lecture Notes in Computational Science and Engineering
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| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I Introduction
- II The Continuous Problem and Its Discretization in Time
- III Convergence of the Discretization in Time and Space
- IV Computational Error Estimation
- V Towards an Effective Algorithm. Practical Issues
- VI Illustrative Numerical Tests
- VII Applications from Computational Sciences
- Appendix A. Advanced Tools from Functional Analysis
- §1. Gelfand Triple
- §2. Sesquilinear Forms and Bounded Operators in Hilbert Spaces
- §3. Unbounded Operators in Hilbert Spaces
- §4. Analytic Semigroups
- §5. Vectorial Functions Defined on Real Intervals
- Appendix B. Consistency and Stability of Rosenbrock Methods
- §1. Order Conditions
- §2. The Stability Function
- §3. The Property ‘Stiffly Accurate’
- Appendix C. Coefficients of Selected Rosenbrock Methods
- Appendix D. Color Plates
- Table of Notations