Ebook: 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 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.

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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.

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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.
Content:
Front Matter....Pages I-XII
Introduction....Pages 1-4
The Continuous Problem and Its Discretization in Time....Pages 5-13
Convergence of the Discretization in Time and Space....Pages 15-29
Computational Error Estimation....Pages 31-45
Towards an Effective Algorithm. Practical Issues....Pages 47-68
Illustrative Numerical Tests....Pages 69-77
Applications from Computational Sciences....Pages 79-117
Back Matter....Pages 119-162

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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.
Content:
Front Matter....Pages I-XII
Introduction....Pages 1-4
The Continuous Problem and Its Discretization in Time....Pages 5-13
Convergence of the Discretization in Time and Space....Pages 15-29
Computational Error Estimation....Pages 31-45
Towards an Effective Algorithm. Practical Issues....Pages 47-68
Illustrative Numerical Tests....Pages 69-77
Applications from Computational Sciences....Pages 79-117
Back Matter....Pages 119-162
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