Error Estimates For Well Balanced Schemes On Simple Balance Laws

Author : Debora Amadori
Publisher : Springer
ISBN 13 : 3319247859
Total Pages : 119 pages
Book Rating : 4.54/5 ( download)

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Download or read book Error Estimates for Well-Balanced Schemes on Simple Balance Laws written by Debora Amadori and published by Springer. This book was released on 2015-10-23 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Edwige Godlewski
Publisher : Springer Nature
ISBN 13 : 1071613448
Total Pages : 846 pages
Book Rating : 4.43/5 ( download)

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Download or read book Numerical Approximation of Hyperbolic Systems of Conservation Laws written by Edwige Godlewski and published by Springer Nature. This book was released on 2021-08-28 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.

Author : Laurent Gosse
Publisher : Springer
ISBN 13 : 3319492624
Total Pages : 362 pages
Book Rating : 4.29/5 ( download)

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Download or read book Innovative Algorithms and Analysis written by Laurent Gosse and published by Springer. This book was released on 2016-05-26 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Clément Cancès
Publisher : Springer
ISBN 13 : 3319573977
Total Pages : 457 pages
Book Rating : 4.77/5 ( download)

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Download or read book Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects written by Clément Cancès and published by Springer. This book was released on 2017-05-23 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier–Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asy mptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is a valuable resource for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.

Author : Dhananjay Singh
Publisher : Springer
ISBN 13 : 9811322392
Total Pages : 70 pages
Book Rating : 4.96/5 ( download)

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Download or read book Signal Processing Applications Using Multidimensional Polynomial Splines written by Dhananjay Singh and published by Springer. This book was released on 2018-12-07 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights new methods, algorithms and software for the digital processing and recovery of signals. In addition, it describes a new method for modeling one dimensional and multidimensional signals as successions of local polynomial splines and their spectral characteristics. It provides examples of how the proposed methods can be applied in specific cases, together with signal processing software examples in the MATLAB environment, and models of special processes in the Simulink environment. The book’s goal is to make it easier for beginners to understand the subject matter; it is intended for engineers, undergraduate and graduate students engaged in research or the evaluation and design of hardware and software for the digital processing and recovery of signals.

Author : Laurent Gosse
Publisher : Springer Science & Business Media
ISBN 13 : 8847028922
Total Pages : 346 pages
Book Rating : 4.20/5 ( download)

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Download or read book Computing Qualitatively Correct Approximations of Balance Laws written by Laurent Gosse and published by Springer Science & Business Media. This book was released on 2013-03-30 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or space-dependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curves being deformed by local averaging steps in Godunov-type schemes, low-order errors propagating along expanding characteristics after having hit a discontinuity, exponential amplification of truncation errors in the presence of accretive source terms... This book aims at presenting rigorous derivations of different, sometimes called well-balanced, numerical schemes which succeed in reconciling high accuracy with a stronger robustness even in the aforementioned accretive contexts. It is divided into two parts: one dealing with hyperbolic systems of balance laws, such as arising from quasi-one dimensional nozzle flow computations, multiphase WKB approximation of linear Schrödinger equations, or gravitational Navier-Stokes systems. Stability results for viscosity solutions of onedimensional balance laws are sketched. The other being entirely devoted to the treatment of weakly nonlinear kinetic equations in the discrete ordinate approximation, such as the ones of radiative transfer, chemotaxis dynamics, semiconductor conduction, spray dynamics or linearized Boltzmann models. “Caseology” is one of the main techniques used in these derivations. Lagrangian techniques for filtration equations are evoked too. Two-dimensional methods are studied in the context of non-degenerate semiconductor models.

Author : Sylvie Benzoni-Gavage
Publisher : Springer Science & Business Media
ISBN 13 : 3540757120
Total Pages : 1117 pages
Book Rating : 4.22/5 ( download)

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Download or read book Hyperbolic Problems: Theory, Numerics, Applications written by Sylvie Benzoni-Gavage and published by Springer Science & Business Media. This book was released on 2008-01-12 with total page 1117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modeling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly.

Author : Heinrich Freistühler
Publisher : Birkhäuser
ISBN 13 : 3034883722
Total Pages : 471 pages
Book Rating : 4.26/5 ( download)

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Download or read book Hyperbolic Problems: Theory, Numerics, Applications written by Heinrich Freistühler and published by Birkhäuser. This book was released on 2012-12-06 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.

Author :
Publisher :
ISBN 13 :
Total Pages : 888 pages
Book Rating : 4.54/5 ( download)

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Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : José A. Romagnoli
Publisher : Elsevier
ISBN 13 : 0080530273
Total Pages : 288 pages
Book Rating : 4.77/5 ( download)

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Download or read book Data Processing and Reconciliation for Chemical Process Operations written by José A. Romagnoli and published by Elsevier. This book was released on 1999-10-25 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer techniques have made online measurements available at every sampling period in a chemical process. However, measurement errors are introduced that require suitable techniques for data reconciliation and improvements in accuracy. Reconciliation of process data and reliable monitoring are essential to decisions about possible system modifications (optimization and control procedures), analysis of equipment performance, design of the monitoring system itself, and general management planning. While the reconciliation of the process data has been studied for more than 20 years, there is no single source providing a unified approach to the area with instructions on implementation. Data Processing and Reconciliation for Chemical Process Operations is that source. Competitiveness on the world market as well as increasingly stringent environmental and product safety regulations have increased the need for the chemical industry to introduce such fast and low cost improvements in process operations. Introduces the first unified approach to this important field Bridges theory and practice through numerous worked examples and industrial case studies Provides a highly readable account of all aspects of data classification and reconciliation Presents the reader with material, problems, and directions for further study