Download or read book Accuracy of Least squares Methods for the Navier Stokes Equations written by Pavel B. Bochev and published by . This book was released on 1993 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Accuracy of Least Squares Methods for the Navier Stokes Equations written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-28 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations. Bochev, Pavel B. and Gunzburger, Max D. Glenn Research Center NCC3-233; RTOP 505-90-5K...
Download or read book Least Squares Finite Element Methods written by Pavel B. Bochev and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.
Download or read book Least squares Solution of Incompressible Navier Stokes Equations with the P version of Finite Elements written by Bo-nan Jiang and published by . This book was released on 1991 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NASA Technical Memorandum written by and published by . This book was released on 1994 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theoretical Study of the Incompressible Navier Stokes Equations by the Least Squares Method written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-13 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis. Jiang, Bo-Nan and Loh, Ching Y. and Povinelli, Louis A. Glenn Research Center NCC3-233; RTOP 505-90-5K...
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Methods for the Numerical Solution of Nonlinear Elliptic Problem written by Roland Glowinski and published by SIAM. This book was released on 2015-11-04 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.
Download or read book Advanced Computational Methods in Science and Engineering written by Barry Koren and published by Springer Science & Business Media. This book was released on 2010-04-29 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.
Download or read book Seventh Copper Mountain Conference on Multigrid Methods written by and published by . This book was released on 1996 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallel Computational Fluid Dynamics 98 written by Chiao-ling Lin and published by Elsevier. This book was released on 1999-05-26 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the papers presented at the Parallel Computational Fluid Dynamics 1998 Conference. The book is focused on new developments and applications of parallel technology. Key topics are introduced through contributed papers and invited lectures. These include typical algorithmic developments, such as: distributed computing, domain decomposition and parallel algorithm. Some of the papers address the evaluations of software and machine performance and software tool environments. The application of parallel computers to complex fluid dynamics problems are also conveyed through sessions such as DNS/LES, combustion and reacting flows, industrial applications, water resources and environmental flows. The editors believe this book will provide many researchers, much beyond those contributing to this volume, with fresh information and reference.
Download or read book High Accuracy Solutions of Incompressible Navier Stokes Equations written by Murli M. Gupta and published by . This book was released on 1990 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Least Squares Finite Element Method written by Bo-nan Jiang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.
Download or read book SIAM Journal on Scientific Computing written by and published by . This book was released on 2007 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computer Algebra in Scientific Computing written by Vladimir P. Gerdt and published by Springer. This book was released on 2013-08-15 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.
Download or read book High Accuracy Computing Methods written by Tapan Sengupta and published by Cambridge University Press. This book was released on 2013-05-16 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: ""Presents methods necessary for high accuracy computing of fluid flow and wave phenomena in single source format using unified spectral theory of computing"--Provided by publisher"--
Download or read book Accuracy of a Deterministic Particle Method for Navier Stokes Equations written by J. P. Choquin and published by . This book was released on 1988 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
