Saddle Point Least Squares and Petrov-galerkin Methods Applied to Reaction-diffusion and Convection-diffusion Equations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Saddle Point Least Squares and Petrov-galerkin Methods Applied to Reaction-diffusion and Convection-diffusion Equations PDF full book. Access full book title Saddle Point Least Squares and Petrov-galerkin Methods Applied to Reaction-diffusion and Convection-diffusion Equations by Daniel Hayes. Download full books in PDF and EPUB format.
Author: Daniel Hayes Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
We present new results on both saddle point least-squares and Petrov-Galerkin methods applied to reaction-diffusion and convection-diffusion equations. In the reaction-diffusion equation, we provide a preconditioner which proves to be efficient and easily implementable in practice. For the convection-diffusion equation, we present an optimal trial norm for both a saddle point least-squares reformulation, as well as an up-winding Petrov-Galerkin method. For the Petrov-Galerkin method in one dimension, we make a connection to a standard streamline upwind Petrov-Galerkin method. We introduce optimal trial norms that enable robust stability analysis of the discretization approach. Furthermore, our discretization methods provide efficient and trustworthy means of approximation. For the two dimensional convection-diffusion equation, we present three methods of discretization. These methods are natural extensions of ideas of the one dimensional problems leading to stabilization and accurate approximation. Numerical results are included to support the theoretical aspects, as well as to give motivation for directions of further research and development.
Author: Daniel Hayes Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
We present new results on both saddle point least-squares and Petrov-Galerkin methods applied to reaction-diffusion and convection-diffusion equations. In the reaction-diffusion equation, we provide a preconditioner which proves to be efficient and easily implementable in practice. For the convection-diffusion equation, we present an optimal trial norm for both a saddle point least-squares reformulation, as well as an up-winding Petrov-Galerkin method. For the Petrov-Galerkin method in one dimension, we make a connection to a standard streamline upwind Petrov-Galerkin method. We introduce optimal trial norms that enable robust stability analysis of the discretization approach. Furthermore, our discretization methods provide efficient and trustworthy means of approximation. For the two dimensional convection-diffusion equation, we present three methods of discretization. These methods are natural extensions of ideas of the one dimensional problems leading to stabilization and accurate approximation. Numerical results are included to support the theoretical aspects, as well as to give motivation for directions of further research and development.
Author: Pavel B. Bochev Publisher: Springer Science & Business Media ISBN: 0387689222 Category : Mathematics Languages : en Pages : 669
Book Description
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.
Author: Alfio Quarteroni Publisher: Springer Science & Business ISBN: 8847055229 Category : Mathematics Languages : en Pages : 668
Book Description
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
Author: Themistocles M. Rassias Publisher: Springer Nature ISBN: 3030313395 Category : Mathematics Languages : en Pages : 694
Book Description
An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.
Author: Jan S Hesthaven Publisher: Springer ISBN: 3319224700 Category : Mathematics Languages : en Pages : 139
Book Description
This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
We present the analysis for the higher order continuous Galerkin-Petrov (cGP) time discretization schemes in combination with the one-level local projection stabilization in space applied to time-dependent convection-diffusion-reaction problems. Optimal a-priori error estimates will be proved. Numerical studies support the theoretical results. Furthermore, a numerical comparison between continuous Galerkin-Petrov and discontinuous Galerkin time discretization schemes will be given.
Author: Daniel Hayes
Author: Daniel Hayes
Author: Sarah Roggendorf
Author: Pavel B. Bochev
Author: ![First-order System Least Squares Methods for Convection-diffusion Equations on Unstructures [sic] Meshes PDF](https://books.google.com/books/content/images/frontcover/QnA-HAAACAAJ?fife=w80-h100)
Author: Tony F. Chan
Author: Alfio Quarteroni
Author: Themistocles M. Rassias
Author: C. N. Vijayaragavan
Author: Jan S Hesthaven
Author: