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Author : Georg May
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (931 download)
Download or read book Adjoint-based Error Estimation and Mesh Adaptation for Hybridized Discontinuous Galerkin Methods written by Georg May and published by . This book was released on 2013 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Woopen
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (912 download)
Download or read book Adjoint-based error estimation and mesh adaption for hybridized discontinuous Galerkin methods written by Michael Woopen and published by . This book was released on 2013 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Johannes Neher
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832530886
Total Pages : 106 pages
Book Rating : 4.8/5 (325 download)
Download or read book A Posteriori Error Estimation for Hybridized Mixed and Discontinuous Galerkin Methods written by Johannes Neher and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a variety of finite element based methods applicable to the discretization of second order elliptic boundary value problems in mixed form. However, it is expensive to solve the resulting discrete linear system due to its size and its algebraic structure. Hybridization serves as a tool to circumvent these difficulties. Furthermore hybridization is an elegant concept to establish connections among various finite element methods. In this work connections between the methods and their hybridized counterparts are established after showing the link between three different formulations of the elliptic model problem. The main part of the work contains the development of a reliable a posteriori error estimator, which is applicable to all of the methods above. This estimator is the key ingredient of an adaptive numerical approximation of the original boundary value problem. Finally, a number of numerical tests is discussed in order to exhibit the performance of the adaptive hybridized methods.
Author : Vít Dolejší
Publisher : Springer Nature
ISBN 13 : 3031042794
Total Pages : 258 pages
Book Rating : 4.0/5 (31 download)
Download or read book Anisotropic hp-Mesh Adaptation Methods written by Vít Dolejší and published by Springer Nature. This book was released on 2022-06-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.
Author : Andrea Cangiani
Publisher : Springer
ISBN 13 : 3319676733
Total Pages : 133 pages
Book Rating : 4.3/5 (196 download)
Download or read book hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes written by Andrea Cangiani and published by Springer. This book was released on 2017-11-27 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios.
Author : Marcus Olavi Rüter
Publisher : Springer Nature
ISBN 13 : 3030061736
Total Pages : 496 pages
Book Rating : 4.0/5 (3 download)
Download or read book Error Estimates for Advanced Galerkin Methods written by Marcus Olavi Rüter and published by Springer Nature. This book was released on 2019-11-07 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.
Author : Christian Klingenberg
Publisher : Springer
ISBN 13 : 3319915487
Total Pages : 698 pages
Book Rating : 4.3/5 (199 download)
Download or read book Theory, Numerics and Applications of Hyperbolic Problems II written by Christian Klingenberg and published by Springer. This book was released on 2018-06-27 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.
Download or read book Robust a Posteriori Error Estimation for Discontinuous Galerkin Methods for Convection Diffusion Problems written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The present thesis is concerned with the development and practical implementation of robust a-posteriori error estimators for discontinuous Galerkin (DG) methods for convection-diffusion problems. It is well-known that solutions to convection-diffusion problems may have boundary and internal layers of small width where their gradients change rapidly. A powerful approach to numerically resolve these layers is based on using hp-adaptive finite element methods, which control and minimize the discretization errors by locally adapting the mesh sizes (h-refinement) and the approximation orders (p-refinement) to the features of the problems. In this work, we choose DG methods to realize adaptive algorithms. These methods yield stable and robust discretization schemes for convection-dominated problems, and are naturally suited to handle local variations in the mesh sizes and approximation degrees as required for hp-adaptivity. At the heart of adaptive finite element methods are a-posteriori error estimators. They provide information on the errors on each element and indicate where local refinement/derefinement should be applied. An efficient error estimator should always yield an upper and lower bound of the discretization error in a suitable norm. For convection-diffusion problems, it is desirable that the estimator is also robust, meaning that the upper and lower bounds differ by a factor that is independent of the mesh Peclet number of the problem. We develop a new approach to obtain robust a-posteriori error estimates for convection-diffusion problems for h-version and hp-version DG methods. The main technical tools in our analysis are new hp-version approximation results of an averaging operator, which are derived for irregular hexahedral meshes in three dimensions, as well as for irregular anisotropic rectangular meshes in two dimensions. We present a series of numerical examples based on C++ implementations of our methods. The numerical results indicate that the erro.
Author :
Publisher : Elsevier
ISBN 13 : 0443294496
Total Pages : 446 pages
Book Rating : 4.4/5 (432 download)
Download or read book Error Control, Adaptive Discretizations, and Applications, Part 1 written by and published by Elsevier. This book was released on 2024-06-29 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error Control, Adaptive Discretizations, and Applications, Volume 58, Part One highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems, An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations. - Covers multi-scale modeling - Includes updates on data-driven modeling - Presents the latest information on large deformations of multi-scale materials
Author : Keigan MacLean
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (126 download)
Download or read book Unstructured Anisotropic All-quad Mesh Adaptation Based on a Continuous Local Error Model for the Discontinuous Galerkin Method written by Keigan MacLean and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This thesis will present a method of unstructured anisotropic adaptation for all-quad mesh suitable for use with high-order methods. The overall goal is to minimize the computational cost needed to perform highly accurate Computational Fluid Dynamics (CFD) simulations. With adaptive methods this can be accomplished through modifying the underlying spatial discretization of the domain. Here, this will be tailored to the particular problem at hand through a continuous local error model. In this form, the physical mesh geometry is replaced by the notion of a frame field, allowing us to extend previous ideas from metric-based adaptation methods. This will serve as a means to restate the discrete error minimization problem in order to determine the target element size and shape based on an optimal distribution of degrees of freedom.Furthermore, the goal of most CFD simulations is to measure some particular output of interest (e.g. such as lift or drag). Therefore, extensions to the method will be examined for goal-oriented adaptation. This involves using the adjoint problem solution and dual-weighted residuals to target mesh refinement in areas most crucial to the accuracy of these measurements.Finally, this work will also consider the implementation of a fully unstructured and anisotropic all-quad mesh generator capable of conforming to the aforementioned target elements. Here, the procedure is based on an Lp-CVT energy minimization problem used to determine updated node positions. Overall, this work will combine each of these aspects in order to establish a complete adaptive framework for use in solving high-order problems with the Discontinuous Galerkin method"--
Author : Rudiger Verfurth
Publisher : Wiley
ISBN 13 : 9780471967958
Total Pages : 134 pages
Book Rating : 4.9/5 (679 download)
Download or read book A Review of Posteriori Error Estimation & Adaptive Mesh-Refinement Techniques written by Rudiger Verfurth and published by Wiley. This book was released on 1996-06-11 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wiley—Teubner Series Advances in Numerical Mathematics Editors Hans Georg Bock Mitchell Luskin Wolfgang Hackbusch Rolf Rannacher A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques Rüdiger Verfürth Ruhr-Universität Bochum, Germany Self-adaptive discretization methods have gained an enormous importance for the numerical solution of partial differential equations which arise in physical and technical applications. The aim of these methods is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools utilised are a posteriori error estimators and indicators which are able to give global and local information on the error of the numerical solution, using only the computed numerical solution and known data of the problem. Presenting the most frequently used error estimators which have been developed by various scientists in the last two decades, this book demonstrates that they are all based on the same basic principles. These principles are then used to develop an abstract framework which is able to handle general nonlinear problems. The abstract results are applied to various classes of nonlinear elliptic partial differential equations from, for example, fluid and continuum mechanics, to yield reliable and easily computable error estimators. The book covers stationary problems but omits transient problems, where theory is often still too complex and not yet well developed.
Author : Martin Juhas
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Adaptive Mesh Refinement Based on a Posteriori Error Estimation written by Martin Juhas and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Indbydelse til Udstillingen af Carl Lochers grafiske Arbejder written by and published by . This book was released on 1919 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ezra Serge Adam Rozier
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (142 download)
Download or read book Error Estimates of Discontinuous Galerkin Methods on Moving Meshes for the Advection-diffusion Equation written by Ezra Serge Adam Rozier and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Troy E. Lake
Publisher :
ISBN 13 : 9780355322934
Total Pages : 77 pages
Book Rating : 4.3/5 (229 download)
Download or read book Adjoint Based, Error Controlled, Loosely Coupled, Unstructured Design Optimization and Adaptive Mesh Refinement Using FUN3D written by Troy E. Lake and published by . This book was released on 2017 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adjoint-based design problems are dependent on the sensitivities from the CFD solution. Current best practices for these adjoint based design problems use fixed-complexity computational meshes that are built using developed best practices. An issue with these fixed-complexity computational meshes is that flow features may not be properly or completely captured. To improve the accuracy of the solution and the sensitivities, the mesh can be adaptively refined to reduce the discretization error within the flow solution. By adapting the mesh, the size of the mesh may be reduced as well, increasing the computational efficiency of the design problem. The computational efficiency of the design problem may also be improved with the use of progressive design variable parameterization. This research focuses on developing methodologies for variations of current best practices methods for design optimization problems including the use of adaptive mesh refinement and progressive design variable parametrization.
Author : S. Prudhomme
Publisher :
ISBN 13 :
Total Pages : 41 pages
Book Rating : 4.:/5 (897 download)
Download or read book Review of a Priori Error Estimation for Discontinuous Galerkin Methods written by S. Prudhomme and published by . This book was released on 2000 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pascal Tremblay
Publisher :
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.:/5 (658 download)
Download or read book Two-dimensional, Three-dimensional and Four-dimensional Anisotropic Mesh Adaptation for the Time-continuous Space-time Finite Element Method with Applications to the Incompressible Navier-Stokes Equations written by Pascal Tremblay and published by . This book was released on 2007 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
