Adaptive Multilevel Solution of Nonlinear Parabolic Pde Systems Theory, Algorithm, and Applications

Another challenge is to develop efficient higher-order one-step integration methods which can handle very stiff equations and which allow us to accommodate a spatial grid in each time step without any specific difficulties. He certainly will forgive me the use of Rosenbrock methods rather than extrapolation methods to integrate in time.

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.