UID:
almahu_9949462261302882
Umfang:
1 online resource (421 p.)
ISBN:
9783110283112
,
9783110238570
Serie:
De Gruyter Textbook
Inhalt:
This book deals with the general topic "Numerical solution of partial differential equations (PDEs)" with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like "Numerical Analysis in Modern Scientific Computing" by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence. Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted. The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.
Anmerkung:
Frontmatter --
,
Preface --
,
Contents --
,
Outline --
,
Chapter 1. Elementary Partial Differential Equations --
,
Chapter 2. Partial Differential Equations in Science and Technology --
,
Chapter 3. Finite Difference Methods for Poisson Problems --
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Chapter 4. Galerkin Methods --
,
Chapter 5. Numerical Solution of Linear Elliptic Grid Equations --
,
Chapter 6. Construction of Adaptive Hierarchical Meshes --
,
Chapter 7. Adaptive Multigrid Methods for Linear Elliptic Problems --
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Chapter 8. Adaptive Solution of Nonlinear Elliptic Problems --
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Chapter 9. Adaptive Integration of Parabolic Problems --
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A Appendix --
,
B Software --
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Bibliography --
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Index
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Mode of access: Internet via World Wide Web.
,
In English.
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012, De Gruyter, 9783110288995
In:
E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012, De Gruyter, 9783110293722
In:
E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012, De Gruyter, 9783110288926
Weitere Ausg.:
ISBN 9783110283105
Sprache:
Englisch
Fachgebiete:
Mathematik
DOI:
10.1515/9783110283112
URL:
https://doi.org/10.1515/9783110283112
URL:
https://www.degruyter.com/isbn/9783110283112
URL:
https://doi.org/10.1515/9783110283112
URL:
https://doi.org/10.1515/9783110283112
