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

Please always quote using this URN: urn:nbn:de:0297-zib-4089
  • This monograph has been written to illustrate the interlocking of theory, algorithm, and application in developing solution techniques for complex PDE systems. A deep theoretical understanding is necessary to produce a powerful idea leading to a successful algorithm. Efficient and robust implementation is the key to make the algorithm perform satisfactorily. The extra insight obtained by solving real--life problems brings out the structure of the method more clearly and suggests often ways to improve the numerical algorithm. It is my intention to impart the beauty and complexity found in both the theoretical investigation of the adaptive algorithm proposed here, i.e., the coupling of Rosenbrock methods in time and multilevel finite elements in space, and its realization. I hope that this method will find many more interesting applications.

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Author:Jens Lang
Document Type:Habilitation
Tag:Adaptive multilevel finite elements; Rosenbrock methods; Rothe method; a posteriori error estimates
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C20 Models, numerical methods [See also 68U20]
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:1999/06/28
Series (Serial Number):ZIB-Report (SC-99-20)
Published in:A rev. vers. appeared as: Jens Lang: Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems : Theory, Algorithm, and Applications. Berlin: Springer 2001. Lecture Notes in Computational Science and Engineering, 16. ISBN 3-540-67900-6
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