Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
This report contains results of analysis done during an FY08 feasibility study investigating the use of adjoint methodologies for a posteriori error estimation for hydrodynamics simulations. We developed an approach to adjoint analysis for these systems through use of modified equations and viscosity solutions. Targeting first the 1D Burgers equation, we include a verification of the adjoint operator for the modified equation for the Lax-Friedrichs scheme, then derivations of an a posteriori error analysis for a finite difference scheme and a discontinuous Galerkin scheme applied to this problem. We include some numerical results showing the use of the error estimate. Lastly, we develop a computable a posteriori error estimate for the MAC scheme applied to stationary Navier-Stokes.
Author: Timothy J. Barth
Publisher: Springer Science & Business Media
ISBN: 3662051893
Category : Mathematics
Languages : en
Pages : 354
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Book Description
As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1278
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Author:
Publisher:
ISBN:
Category : Numerical analysis
Languages : en
Pages : 1156
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Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 348
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Author:
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 838
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Book Description
Author: Dan G. Cacuci
Publisher: CRC Press
ISBN: 0203498798
Category : Mathematics
Languages : en
Pages : 304
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Book Description
As computer-assisted modeling and analysis of physical processes have continued to grow and diversify, sensitivity and uncertainty analyses have become indispensable investigative scientific tools in their own right. While most techniques used for these analyses are well documented, there has yet to appear a systematic treatment of the method based
Author: American Geophysical Union. Meeting
Publisher:
ISBN:
Category : Geophysics
Languages : en
Pages : 1148
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Book Description
Author: Ivo Babuška
Publisher: Oxford University Press
ISBN: 9780198502760
Category : Mathematics
Languages : en
Pages : 820
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Book Description
The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand are at the forefront of engineering and theoretical interests. This book presents the mathematical theory of the finite element method and is the first to focus on the questions of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.
Author: Peter Benner
Publisher: SIAM
ISBN: 161197481X
Category : Science
Languages : en
Pages : 421
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Book Description
Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.
