Download or read book Optimum Mixed Finite Element Nonlinear Galerkin Method for the Navier Stokes Equations written by and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Conforming Mixed Finite Element Methods for the Inhomogeneous Stationary Navier Stokes Equations written by Max D. Gunzburger and published by . This book was released on 1982 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We consider the stationary Navier-Stokes equations in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, we prove the existence and uniqueness of the solution of a weak formulation of the equations. Next, a conforming mixed finite element method is presented and optimal estimates for the error of the approximate solution are provided. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are analyzed. Numerical examples, using an efficient choice of finite element spaces, are also provided" -- abstract.

Download or read book Development of Versatile Mixed Finite Element Methods for the Non Isothermal Incompressible and Compressible Navier Stokes Equations written by Edward Miller and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ever increasing demand for accurate numerical methods has led to the development of more and more sophisticated methods for simulating fluid flow. These methods are often designed to handle a specific flow regime or be valid under specific circumstances. What is needed in the field is a method that is accurate and robust over a wide range of conditions. Here, we propose a finite element method designed to work over a broad range of flow regimes and remain consistent and accurate in each regime. This is accomplished utilizing a mixed finite element method whose properties are rigorously analyzed to demonstrate the method's effectiveness at handling these different flow regimes. We first use standard mathematical techniques to prove that the method is stable and obtains optimal error estimates for the non-isothermal incompressible Navier-Stokes equations. We then demonstrate on a series of test cases that the method accurately captures the physics of the non-isothermal incompressible Navier-Stokes equations. Next, we extend our method to the compressible Navier-Stokes equations where again the order of accuracy is demonstrated, this time using a series of numerical experiments. Finally, we present a series of compressible flow test cases to prove that the method can capture the physics of this regime.

Download or read book The Least Squares Finite Element Method written by Bo-nan Jiang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.

Download or read book finite element methods written by Michel Krizek and published by CRC Press. This book was released on 2016-04-19 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings originated from a conference commemorating the 50th anniversary of the publication of Richard Courant's seminal paper, Variational Methods for Problems of Equilibrium and Vibration. These papers address fundamental questions in numerical analysis and the special problems that occur in applying the finite element method to various

Download or read book Robust Arbitrary Order Mixed Finite Element Methods for the Incompressible Stokes Equations written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Standard mixed finite element methods for the incompressible Navier-Stokes equations that relax the divergence constraint are not robust against large irrotational forces in the momentum balance and the velocity error depends on the continuous pressure. This robustness issue can be completely cured by using divergence-free mixed finite elements which deliver pressure-independent velocity error estimates. However, the construction of H1-conforming, divergence-free mixed finite element methods is rather difficult. Instead, we present a novel approach for the construction of arbitrary order mixed finite element methods which deliver pressure-independent velocity errors. The approach does not change the trial functions but replaces discretely divergence-free test functions in some operators of the weak formulation by divergence-free ones. This modification is applied to inf-sup stable conforming and nonconforming mixed finite element methods of arbitrary order in two and three dimensions. Optimal estimates for the incompressible Stokes equations are proved for the H1 and L2 errors of the velocity and the L2 error of the pressure. Moreover, both velocity errors are pressure-independent, demonstrating the improved robustness. Several numerical examples illustrate the results.

Download or read book Projection and Quasi Compressibility Methods for Solving the Incompressible Navier Stokes Equations written by and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. '... this book should be mandatory reading for applied mathematicians specializing in computational fluid dynamics.' J.-L.Guermond. Mathematical Reviews, Ann Arbor

Download or read book A Mixed Finite Element Method for the Navier Stokes Equations written by Pierre-Arnaud Raviart and published by . This book was released on 1977 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Elements and Fast Iterative Solvers written by Howard C. Elman and published by . This book was released on 2014 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory" provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

Download or read book Finite Elements and Fast Iterative Solvers written by Howard Elman and published by OUP Oxford. This book was released on 2014-06-19 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

Download or read book Partial Differential Equations written by Roland Glowinski and published by Springer Science & Business Media. This book was released on 2008-06-26 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.

Download or read book Finite Element Solutions of Axisymmetric Navier Stokes Equations for Non isothermal Flows with Swirl written by ShuShi Huang and published by . This book was released on 1996 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Volume Methods for the Incompressible Navier Stokes Equations written by Jian Li and published by Springer Nature. This book was released on 2022-01-20 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to provide a comprehensive understanding of the most recent developments in finite volume methods. Its focus is on the development and analysis of these methods for the two- and three-dimensional Navier-Stokes equations, supported by extensive numerical results. It covers the most used lower-order finite element pairs, with well-posedness and optimal analysis for these finite volume methods.The authors have attempted to make this book self-contained by offering complete proofs and theoretical results. While most of the material presented has been taught by the authors in a number of institutions over the past several years, they also include several updated theoretical results for the finite volume methods for the incompressible Navier-Stokes equations. This book is primarily developed to address research needs for students and academic and industrial researchers. It is particularly valuable as a research reference in the fields of engineering, mathematics, physics, and computer sciences.

Download or read book Least Squares Finite Element Methods written by Pavel B. Bochev and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Discrete and Continuous Dynamical Systems written by and published by . This book was released on 2007 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.