Error Estimates for Well Balanced Schemes on Simple Balance Laws

Author: Debora Amadori
Publisher: Springer
ISBN: 3319247859
Format: PDF
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This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.

Multi dimensional Hyperbolic Partial Differential Equations

Author: Sylvie Benzoni-Gavage
Publisher: Oxford University Press on Demand
ISBN: 019921123X
Format: PDF, Docs
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Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.

Innovative Algorithms and Analysis

Author: Laurent Gosse
Publisher: Springer
ISBN: 3319492624
Format: PDF, ePub, Docs
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This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016. The event brought together many prominent researchers in both Mathematical Analysis and Numerical Computing, the goal being to promote interdisciplinary collaborations. Accordingly, the following thematic areas were developed: 1. Lagrangian discretizations and wavefront tracking for synchronization models; 2. Astrophysics computations and post-Newtonian approximations; 3. Hyperbolic balance laws and corrugated isometric embeddings; 4. “Caseology” techniques for kinetic equations; 5. Tentative computations of compressible non-standard solutions; 6. Entropy dissipation, convergence rates and inverse design issues. Most of the articles are presented in a self-contained manner; some highlight new achievements, while others offer snapshots of the “state of the art” in certain fields. The book offers a unique resource, both for young researchers looking to quickly enter a given area of application, and for more experienced ones seeking comprehensive overviews and extensive bibliographic references.

Variational and Topological Methods in the Study of Nonlinear Phenomena

Author: Vieri Benci
Publisher: Birkhauser
Format: PDF, ePub
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This volume covers recent advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological methods.A broad range of topics is covered, including: * concentration phenomena in pdes* variational methods with applications to pdes and physics* periodic solutions of odes* computational aspects in topological methods* mathematical models in biologyThough well-differentiated, the topics covered are unified through a common perspective and approach. Unique to the work are several chapters on computational aspects and applications to biology, not usually found with such basic studies on pdes and odes. The volume will be an excellent reference text for researchers and graduate students in the above mentioned fields.Contributors: M. Clapp, M. Del Pino, M. Esteban, P. Felmer, A. Ioffe, W. Marzantowicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, E. Sere, P. Sintzoff, R. Turner, M. Willem