Download or read book A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial differential equation Outputs written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1998 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Posteriori Finite Element Bounds for Linear functional Outputs of Coercive Partial Differential Equations and of the Stokes Problem written by Marius Paraschivoiu and published by . This book was released on 1997 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Posteriori Error Estimation Techniques for Finite Element Methods written by Rüdiger Verfürth and published by OUP Oxford. This book was released on 2013-04-18 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computed from the given numerical solution and the data of the differential equation. This book reviews the most frequently used a posteriori error estimation techniques and applies them to a broad class of linear and nonlinear elliptic and parabolic equations. Although there are various approaches to adaptivity and a posteriori error estimation, they are all based on a few common principles. The main aim of the book is to elaborate these basic principles and to give guidelines for developing adaptive schemes for new problems. Chapters 1 and 2 are quite elementary and present various error indicators and their use for mesh adaptation in the framework of a simple model problem. The basic principles are introduced using a minimal amount of notations and techniques providing a complete overview for the non-specialist. Chapters 4-6 on the other hand are more advanced and present a posteriori error estimates within a general framework using the technical tools collected in Chapter 3. Most sections close with a bibliographical remark which indicates the historical development and hints at further results.

Download or read book Design Sensitivity Analysis written by Lisa G. Stanley and published by SIAM. This book was released on 2002-01-01 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrates some of the important issues inherent in using the sensitivity equation method for PDEs.

Download or read book A Posteriori Finite Element Bounds with Adaptive Mesh Refinement Application to Outputs of the Three Dimensional Convection diffusion Equation written by Hae-Won Choi and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulations based on an 'a posteriori' finite element bound method with adaptive mesh refinement is presented for linear-functional outputs of the convection-diffusion equation in three spaces dimensions. The bound method is based upon the construction of an augmented Lagrangian, in which the objective is an energy reformulation of the desired output, and the constraints are the finite element equilibrium equations and inter-subdomain continuity requirements. Outputs are functionals of the field solution obtained from partial differential equations. The bound method provides relevant, quantitative, inexpensive. And rigorous bounds to the output on a very fine discretization at a cost of the coarse mesh calculation. To achieve a derived accuracy of the bound gap at a reasonable coat, an adaptive mesh refinement technique is used to refine the mesh only where high resolution is needed. Optimal stabilization parameter [kappa]* is also studied. This parameter improves the bounds, i.e. improves the sharpness of the bound gap. Finally the hybrid flux calculations on the coarse "working" mesh are compared with that on the fine "truth" mesh.

Download or read book Advances in a Posteriori Error Estimation on Anisotropic Finite Element Discretizations written by Gerd Kunert and published by Logos Verlag Berlin. This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Certain classes of partial differential equations generically give rise to solutions with strong directional features, e.g. with boundary layers. Such solutions are called anisotropic. Their discretization by means of the finite element method (for example) can favourably employ so-called anisotropic meshes. These meshes are characterized by stretched, anisotropic finite elements with a (very) large stretching ratio. The widespread use of computer simulation leads to an increasing demand for semi- or fully automatic solution procedures. Within such self-adaptive algorithms, a posteriori error estimators form an indispensable ingredient for quality control. They are well understood for standard, isotropic discretizations. The knowledge about a posteriori error estimation on anisotropic meshes is much less mature. During the last decade the foundation and basic principles have been proposed, discussed and established, mostly for the Poisson problem. This monograph summarises some of the recent advances in anisotropic error estimation for more challenging problems. Emphasis is given to the contributions of the author. In Chapter 3 the investigation starts with singularly perturbed reaction diffusion problems which frequently lead to solutions with boundary layers. This problem class often arises when simplifying more complex models. Chapter 4 treats singularly perturbed convection diffusion problems, i.e. the convection is dominating. The solution structure is more intricate, and often features boundary layer and/or interior layer solutions. Chapter 5 is devoted to the Stokes equations. Flow problems generically give rise to anisotropic solutions (e.g. with edge singularities or containing layers). The Stokes equations often serve as a simplified or linearised model. In all three chapters, the main results consist in error estimators and corresponding error bounds that are robust with respect to the mesh anisotropy, as far as possible. Finally Chapter 6 addresses the robustness of a posteriori error estimation with respect to the mesh anisotropy.In particular the relation between anisotropic mesh construction and error estimation is investigated. This thesis presents the philosophy of anisotropic error estimation as well as the main results and the definitions required. Proofs and technical details are omitted; instead the key ideas are explained.The compact style of presentation aims at practitioners in particular by providing easily accessible error estimators and error bounds. Further insight is readily possible through the references.

Download or read book Industrial and Environmental Applications of Direct and Large Eddy Simulation written by Sedat Biringen and published by Springer. This book was released on 1999-08-19 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique assembly of state-of-the-art articles concerned with a wide range of fundamental and applied issues, including turbulence parameterization, numerical uncertainty, complex turbulence, flow-structure interactions, atmosphere-ocean turbulence and turmachinery flows. The articles provide specific examples of the most recent applications of direct and large eddies methods. These methods have been very successful in providing new insight into the structure of turbulent flows and are becoming feasable in real engineering and environmental problems with complex geometries. This volume will be a very valuable source book for researchers and graduate students embarking on studies in turbulent flow simulation.

Download or read book Computational Methods for Optimal Design and Control written by J. Borggaard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Second International Workshop on Optimal Design and Control, held in Arlington, Virginia, 30 September-3 Octo ber, 1997. The First Workshop was held in Blacksburg, Virginia in 1994. The proceedings of that meeting also appeared in the Birkhauser series on Progress in Systems and Control Theory and may be obtained through Birkhauser. These workshops were sponsored by the Air Force Office of Scientific Re search through the Center for Optimal Design and Control (CODAC) at Vrrginia Tech. The meetings provided a forum for the exchange of new ideas and were designed to bring together diverse viewpoints and to highlight new applications. The primary goal of the workshops was to assess the current status of research and to analyze future directions in optimization based design and control. The present volume contains the technical papers presented at the Second Workshop. More than 65 participants from 6 countries attended the meeting and contributed to its success. It has long been recognized that many modern optimal design problems are best viewed as variational and optimal control problems. Indeed, the famous problem of determining the body of revolution that produces a minimum drag nose shape in hypersonic How was first proposed by Newton in 1686. Optimal control approaches to design can provide theoretical and computational insight into these problems. This volume contains a number of papers which deal with computational aspects of optimal control.

Download or read book Numerical Data Fitting in Dynamical Systems written by Klaus Schittkowski and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.

Download or read book A Posteriori Bounds on Linear Functionals of Coercive 2nd Order PDEs Using Discontinuous Galerkin Methods written by Joseph Sze Hsuan Wong and published by . This book was released on 2006 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we extend current capabilities in producing error bounds on the exact linear functionals of linear partial differential equations in a number of ways. Unlike previous approaches, we base our method on the Discontinuous Galerkin finite element method. For equations such as the convection-diffusion equation, the convection term is handled by the standard DG method for hyperbolic problems while the diffusion operator is discretized by the LDG scheme. This choice allows for the effective bounding of outputs associated with high Peclect number problems without resolving all of the details of the solution. In addition to the ability to manage convection dominated problems, we expand the scope of our error bounding algorithm beyond present capabilities to include saddle problems such as the incompressible Stokes equations. Apart from the aforementioned advantages, the DG discretization employed here also produces associated numerical fluxes, which make the complicated "equilibration" procedure that is often necessary in implicit a-posteriori algorithms, unnecessary.

Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on 1999-07 with total page 1154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book ICASE Semiannual Report written by and published by . This book was released on 1998 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book NASA Langley Scientific and Technical Information Output 1998 written by and published by . This book was released on 1999 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Aspects of Finite Elements in Partial Differential Equations written by Carl de Boor and published by Academic Press. This book was released on 2014-05-10 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Aspects of Finite Elements in Partial Differential Equations addresses the mathematical questions raised by the use of finite elements in the numerical solution of partial differential equations. This book covers a variety of topics, including finite element method, hyperbolic partial differential equation, and problems with interfaces. Organized into 13 chapters, this book begins with an overview of the class of finite element subspaces with numerical examples. This text then presents as models the Dirichlet problem for the potential and bipotential operator and discusses the question of non-conforming elements using the classical Ritz- and least-squares-method. Other chapters consider some error estimates for the Galerkin problem by such energy considerations. This book discusses as well the spatial discretization of problem and presents the Galerkin method for ordinary differential equations using polynomials of degree k. The final chapter deals with the continuous-time Galerkin method for the heat equation. This book is a valuable resource for mathematicians.

Download or read book Finite Element Error Analysis for PDE constrained Optimal Control Problems written by Dieter Sirch and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subject of this work is the analysis of numerical methods for the solution of optimal control problems governed by elliptic partial differential equations. Such problems arise, if one does not only want to simulate technical or physical processes but also wants to optimize them with the help of one or more influence variables. In many practical applications these influence variables, so called controls, cannot be chosen arbitrarily, but have to fulfill certain inequality constraints. The numerical treatment of such control constrained optimal control problems requires a discretization of the underlying infinite dimensional function spaces. To guarantee the quality of the numerical solution one has to estimate and to quantify the resulting approximation errors. In this thesis a priori error estimates for finite element discretizations are proved in case of corners or edges in the underlying domain and nonsmooth coefficients in the partial differential equation. These facts influence the regularity properties of the solution and require adapted meshes to get optimal convergence rates. Isotropic and anisotropic refinement strategies are given and error estimates in polygonal and prismatic domains are proved. The theoretical results are confirmed by numerical tests.

Download or read book 38th Aerospace Sciences Meeting and Exhibit written by and published by . This book was released on 2000 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Frontiers of Computational Fluid Dynamics 1998 written by David A. Caughey and published by World Scientific. This book was released on 1998 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of Frontiers of Computational Fluid Dynamics was published in 1994 and was dedicated to Prof Antony Jameson. The present volume is dedicated to Prof Earll Murman in appreciation of his original contributions to this field.The book covers the following topics: Transonic and Hypersonic AerodynamicsAlgorithm Developments and Computational TechniquesImpact of High Performance ComputingApplications in Aeronautics and BeyondIndustrial PerspectivesEngineering EducationThe book contains 25 chapters written by leading researchers from academia, government laboratories, and industry