Author	Lang, Jens. author
Title	Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems [electronic resource] : Theory, Algorithm, and Applications / by Jens Lang
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001
Connect to	http://dx.doi.org/10.1007/978-3-662-04484-1
Descript	XII, 162 p. 52 illus. online resource

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 Rosenbrock-type one-step methods and multilevel finite elements is analysed. Implementation and efficiency issues are discussed. Special emphasis is put on the solution of real-life applications that arise in today's chemical industry, semiconductor-device fabrication and health care. The book is intended for graduate students and researchers who are either interested in the theoretical understanding of instationary PDE solvers or who want to develop computer codes for solving complex PDEs

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 -- ยง1. Gelfand Triple -- ยง2. Sesquilinear Forms and Bounded Operators in Hilbert Spaces -- ยง3. Unbounded Operators in Hilbert Spaces -- ยง4. Analytic Semigroups -- ยง5. Vectorial Functions Defined on Real Intervals -- Appendix B. Consistency and Stability of Rosenbrock Methods -- ยง1. Order Conditions -- ยง2. The Stability Function -- ยง3. The Property โ{128}{152}Stiffly Accurateโ{128}{153} -- Appendix C. Coefficients of Selected Rosenbrock Methods -- Appendix D. Color Plates -- Table of Notations