Download or read book Stabilised Mixed Finite Element Methods on Anisotropic Meshes written by Andreas Wachtel and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Anisotropic Finite Elements Local Estimates and Applications written by Thomas Apel and published by . This book was released on 1999-07 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book BEM based Finite Element Approaches on Polytopal Meshes written by Steffen Weißer and published by Springer. This book was released on 2019-07-18 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element approaches employs implicitly defined trial functions, which are treated locally by means of boundary integral equations. A detailed construction of high-order approximation spaces is discussed and applied to uniform, adaptive and anisotropic polytopal meshes. The main benefits of these general discretizations are the flexible handling they offer for meshes, and their natural incorporation of hanging nodes. This can especially be seen in adaptive finite element strategies and when anisotropic meshes are used. Moreover, this approach allows for problem-adapted approximation spaces as presented for convection-dominated diffusion equations. All theoretical results and considerations discussed in the book are verified and illustrated by several numerical examples and experiments. Given its scope, the book will be of interest to mathematicians in the field of boundary value problems, engineers with a (mathematical) background in finite element methods, and advanced graduate students.
Download or read book A Simple Introduction to the Mixed Finite Element Method written by Gabriel N. Gatica and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.
Download or read book Finite Element Mesh Generation written by Daniel S.H. Lo and published by CRC Press. This book was released on 2015-01-15 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highlights the Progression of Meshing Technologies and Their Applications Finite Element Mesh Generation provides a concise and comprehensive guide to the application of finite element mesh generation over 2D domains, curved surfaces, and 3D space. Organised according to the geometry and dimension of the problem domains, it develops from the basic meshing algorithms to the most advanced schemes to deal with problems with specific requirements such as boundary conformity, adaptive and anisotropic elements, shape qualities, and mesh optimization. It sets out the fundamentals of popular techniques, including: Delaunay triangulation Advancing-front (ADF) approach Quadtree/Octree techniques Refinement and optimization-based strategies From the geometrical and the topological aspects and their associated operations and inter-relationships, each approach is vividly described and illustrated with examples. Beyond the algorithms, the book also explores the practice of using metric tensor and surface curvatures for generating anisotropic meshes on parametric space. It presents results from research including 3D anisotropic meshing, mesh generation over unbounded domains, meshing by means of intersection, re-meshing by Delaunay-ADF approach, mesh refinement and optimization, generation of hexahedral meshes, and large scale and parallel meshing, along with innovative unpublished meshing methods. The author provides illustrations of major meshing algorithms, pseudo codes, and programming codes in C++ or FORTRAN. Geared toward research centers, universities, and engineering companies, Finite Element Mesh Generation describes mesh generation methods and fundamental techniques, and also serves as a valuable reference for laymen and experts alike.
Download or read book Stabilised Mixed Finite Element Methods written by David Silvester and published by . This book was released on 1995 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mixed Finite Element Technologies written by Peter Wriggers and published by Springer Science & Business Media. This book was released on 2009-06-16 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixed finite element methods are a tool to solve complex engineering problems of different nature. This subject is treated in the volume from the engineering and the mathematical point. Different applications are considered which depict the value of mixed formulations in engineering on one side. On the other side the mathematical background is provided including proofs of convergence and stability of these methods and adequate solvers for mixed problems are discussed. This broad spectrum yields an indepth treatment of mixed methods from different perspectives.
Download or read book Mixed and Hybrid Finite Element Methods written by Franco Brezzi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.
Download or read book Mixed Finite Element Method written by Apostol Poceski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, based on 16 years of work on the finite element method, the author presents the essence of a new, direct approach to the FEM. The work is focused on the mixed method and shows how reliable results may be obtained with fewer equations than usual. The basic principles, the fundamentals and the essence of the FEM are presented, then the method is applied to the analysis of one, two, and three-dimensional problems. It is shown that mixed elements offer superior accuracy compared with stiffness elements. Finally, some new achievements and perspectives for further development are presented. The book is intended for undergraduate and graduate students, mathematicians, research engineers and practicing engineers. To understand the book, a familiarity with classical mechanics is sufficient.
Download or read book The Hybrid High Order Method for Polytopal Meshes written by Daniele Antonio Di Pietro and published by Springer Nature. This book was released on 2020-04-03 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to the design and analysis of Hybrid High-Order methods for diffusive problems, along with a panel of applications to advanced models in computational mechanics. Hybrid High-Order methods are new-generation numerical methods for partial differential equations with features that set them apart from traditional ones. These include: the support of polytopal meshes, including non-star-shaped elements and hanging nodes; the possibility of having arbitrary approximation orders in any space dimension; an enhanced compliance with the physics; and a reduced computational cost thanks to compact stencil and static condensation. The first part of the monograph lays the foundations of the method, considering linear scalar second-order models, including scalar diffusion – possibly heterogeneous and anisotropic – and diffusion-advection-reaction. The second part addresses applications to more complex models from the engineering sciences: non-linear Leray-Lions problems, elasticity, and incompressible fluid flows. This book is primarily intended for graduate students and researchers in applied mathematics and numerical analysis, who will find here valuable analysis tools of general scope.
Download or read book Mixed Finite Element Methods and Applications written by Daniele Boffi and published by Springer. This book was released on 2013-07-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.
Download or read book Mesh Free Methods written by G.R. Liu and published by CRC Press. This book was released on 2002-07-29 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now,
Download or read book Anisotropic mesh adaptation and stabilized finite elements method for solving conjugate heat transfers and turbulent flows written by M. Jérémy Veysset and published by . This book was released on 2014 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The GETMe Mesh Smoothing Framework written by Dimitris P. Vartziotis and published by CRC Press. This book was released on 2018-12-07 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: High quality meshes play a key role in many applications based on digital modeling and simulation. The finite element method is a paragon for such an approach and it is well known that quality meshes can significantly improve computational efficiency and solution accuracy of this method. Therefore, a lot of effort has been put in methods for improving mesh quality. These range from simple geometric approaches, like Laplacian smoothing, with a high computational efficiency but possible low resulting mesh quality, to global optimization-based methods, resulting in an excellent mesh quality at the cost of an increased computational and implementational complexity. The geometric element transformation method (GETMe) aims to fill the gap between these two approaches. It is based on geometric mesh element transformations, which iteratively transform polygonal and polyhedral elements into their regular counterparts or into elements with a prescribed shape. GETMe combines a Laplacian smoothing-like computational efficiency with a global optimization-like effectiveness. The method is straightforward to implement and its variants can also be used to improve tangled and anisotropic meshes. This book describes the mathematical theory of geometric element transformations as foundation for mesh smoothing. It gives a thorough introduction to GETMe-based mesh smoothing and its algorithms providing a framework to focus on effectively improving key mesh quality aspects. It addresses the improvement of planar, surface, volumetric, mixed, isotropic, and anisotropic meshes and addresses aspects of combining mesh smoothing with topological mesh modification. The advantages of GETMe-based mesh smoothing are demonstrated by the example of various numerical tests. These include smoothing of real world meshes from engineering applications as well as smoothing of synthetic meshes for demonstrating key aspects of GETMe-based mesh improvement. Results are compared with those of other smoothing methods in terms of runtime behavior, mesh quality, and resulting finite element solution efficiency and accuracy. Features: • Helps to improve finite element mesh quality by applying geometry-driven mesh smoothing approaches. • Supports the reader in understanding and implementing GETMe-based mesh smoothing. • Discusses aspects and properties of GETMe smoothing variants and thus provides guidance for choosing the appropriate mesh improvement algorithm. • Addresses smoothing of various mesh types: planar, surface, volumetric, isotropic, anisotropic, non-mixed, and mixed. • Provides and analyzes geometric element transformations for polygonal and polyhedral elements with regular and non-regular limits. • Includes a broad range of numerical examples and compares results with those of other smoothing methods.
Download or read book Advanced Finite Element Technologies written by Jörg Schröder and published by Springer. This book was released on 2016-05-19 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.
Download or read book Numerical Methods for Mixed Finite Element Problems written by Jean Deteix and published by Springer Nature. This book was released on 2022-09-24 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on iterative solvers and preconditioners for mixed finite element methods. It provides an overview of some of the state-of-the-art solvers for discrete systems with constraints such as those which arise from mixed formulations. Starting by recalling the basic theory of mixed finite element methods, the book goes on to discuss the augmented Lagrangian method and gives a summary of the standard iterative methods, describing their usage for mixed methods. Here, preconditioners are built from an approximate factorisation of the mixed system. A first set of applications is considered for incompressible elasticity problems and flow problems, including non-linear models. An account of the mixed formulation for Dirichlet’s boundary conditions is then given before turning to contact problems, where contact between incompressible bodies leads to problems with two constraints. This book is aimed at graduate students and researchers in the field of numerical methods and scientific computing.
Download or read book Theory and Practice of Finite Elements written by Alexandre Ern and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.
