Download or read book Finite Element Methods for a Strongly Damped Wave Equation written by Stig Larsson and published by . This book was released on 1989 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Expansions and Extrapolations of H1 Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Wave Finite Element Method written by Boris F. Shorr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational mechanics, as a science employed for the numerical model ing of processes in nature and engineering, has over the last few decades developed two strands. The first concerns the putting of more and more powerful software packages into computational practice, using increas ingly high-performance computers with increasingly large memory. The traditional finite element and finite difference approaches are still preva lent. Over the years however, researchers have met with new problems; their solutions on the basis of traditional methods are at best difficult and at worst impossible to obtain. Such problems provided a powerful impetus in the development of the second strand, resulting in the development of es sentially new approaches for numerical modeling, for example meshless methods, "molecular" dynamics, neuron networks. The current state of the art formed the basis of many papers presented at the Fifth World Congress on Computational Mechanics, Vienna 2002. It is within the framework of the second strand that this book has been written.
Download or read book Adaptive Finite Element Methods for the Damped Wave Equation written by Catherine Wilkins and published by . This book was released on 1998 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomée and published by Springer Science & Business Media. This book was released on 2010 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations written by Gary Cohen and published by Springer. This book was released on 2016-08-05 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulationof waves.
Download or read book Error Estimates for Semidiscrete Galerkin and Fully Discrete Backward Euler Finite Element Schemes for Second Order Strongly Damped Wave Equations written by Sergio Loch and published by . This book was released on 1993 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Birkhäuser. This book was released on 2013-11-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
Download or read book A Finite Element Approach for Wave Propagation in Elastic Solids written by Arkadiusz Żak and published by Springer Nature. This book was released on with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations written by Abdul Kadir Aziz and published by . This book was released on 1972 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations.
Download or read book Transactions of the Army Conference on Applied Mathematics and Computing written by and published by . This book was released on 1991 with total page 930 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Strongly Damped Wave Equation with Constraint written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A weak formulation for the so-called semilinear strongly damped wave equation with constraint is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in Sobolev-Bochner spaces, aimed at providing a suitable "relaxation" of the constraint term. A global in time existence result is proved under the natural condition that the initial data have finite "physical" energy.
Download or read book Evolution Equations Control Theory and Biomathematics written by Philippe Clement and published by CRC Press. This book was released on 1993-11-23 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the Third International Workshop Conference on Evolution Equations, Control Theory and Biomathematics, held in Hans-sur-Lesse, Belgium. The papers examine important advances in evolution equations related to physical, engineering and biological applications.
Download or read book Finite Element Methods written by Jonathan Whiteley and published by Springer. This book was released on 2018-07-13 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Method written by Sinan Muftu and published by Elsevier. This book was released on 2022-07-19 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Method: Physics and Solution Methods enables the reader to develop a sound understanding of physical systems so that they can get the most out of their use of the finite element method. Nearly all physical systems in the FEM realm are represented by partial differential equations. This book focuses on 1D and 2D elasticity, and 1D and 2D heat transfer problems, with a detailed derivation of the governing equations. The connections between the classical variational techniques and the finite element method are carefully explained. After a chapter addressing the classical variational methods, the finite element method is developed as a natural outcome of these methods where the governing PDE is defined over a sub-segment (element) of the solution domain. As well as being an invaluable guide to thorough and effective use of the finite element method, this book also functions as an authoritative reference on theory of elasticity, heat transfer and mechanics of beams and plates.
Download or read book Exponentially Convergent Algorithms for Abstract Differential Equations written by Ivan Gavrilyuk and published by Springer Science & Business Media. This book was released on 2011-07-17 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients. For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems.
