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 Conforming and Nonconforming Finite Element Methods of Streamline Diffusion Type for Solving the Stationary Navier Stokes Equations written by Lutz Tobiska and published by . This book was released on 1990 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Conforming Mixed Finite Element Methods for Incompressible Viscous Flow Problems written by Max D. Gunzburger and published by . This book was released on 1981 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Elements written by D.L. Dwoyer and published by Springer. This book was released on 2013-12-20 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the proceedings ofthe ICASE/LaRC workshop on "Finite Element Theory and Application" held during July 28-30, 1986. The purpose of this workshop was to provide an update on the status of finite element theory, to assess the impactoftbis theory on practice, and to suggest directions for Cuture research. There were thirteen participants in the workshop. Some of them were leading mathematicians working on the finite element theory, and the rest expert practitioners in the areas of fluid dynamics and structural analysis. The first six articles in this volume provide a brief review of the theoretical and computational aspects of finite element methods (FEM). The remaining seven articles deal with a variety of applications highlighting the type of results that are possible, and indicating areas which deserve future research. The first article is by Temam. lt provides an introduction and overview of the general finite element methods for the nonspecialist. lt also illustrates the power of finite element methods with two specific applications-the free surface flowjstructure interaction problern and the compressible Euler solu tion to the flow past a finite aspect ratio flat plate at incidence. The second article by Brezzi is againan introduction and overview ofmixed finite element methods. lt includes a brief discussion of special techniques for solving the discrete problem, as weil as some applications to certain basic problems in elasticity and hydrodynamics.

Download or read book Conforming and Nonconforming Finite Element Methods for Solving the Stationary Stokes Equations written by Michel Crouzeix and published by . This book was released on 1973 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Mathematical Aspects of Finite Element Methods for Incompressible Viscous Flows written by M. D. Gunzburger and published by . This book was released on 1986 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: We survey some mathematical aspects of finite element methods for incompressible viscous flows, concentrating on the steady primitive variable formulation. We address the discretization of a weak formulation of the Navier Stokes equations; we then consider the div-stability condition, whose satisfaction insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

Download or read book Implementation of Finite Element Methods for Navier Stokes Equations written by F. Thomasset and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.

Download or read book Finite Elements in Water Resources written by J. P. Laible and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 805 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the edited proceedings of the Fifth International Conference on Finite Elements in Water Resources, held at the University of Vermont, USA in June 1984. This Conference cont inues the successful series started at Princeton University in 1976, followed by the Conference in Imperial College, London, UK in 1978, the third Conference at the University of Mississippi, USA in 1980 and the fourth at the University of Hannover, Germany in 1982. The objective of this Conference is to provide engineers and scientists interested in water resources with the state-of-t- art on finite element modelling. The Proceedings review the basic theory and applications of the technique in groundwater and seepage, transport phenomena, viscous flow, river, lake and ocean modelling. The fundamentals of the numerical techniques employed in finite elements are also discussed. Many applications illus trate the versatility and generality of the Finite Element Method for the simulation of a wide range of problems in water resources. More recent schemes, in particular, boundary elements, are also presented, together with a series of advanced numerical techniques. The Conference has become an internationally accepted forum for the presentation of new developments of finite elements in water resources techniques. Because of this, a large number of abstracts were submitted to the Organizing Committee and it is our only reg ret that it was impossible to accept all these contributions. The overwhelming response to our Call for Papers has ensured the high quality of these proceedings.

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 Element Methods and Navier Stokes Equations written by C. Cuvelier and published by Springer Science & Business Media. This book was released on 1986-03-31 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Mixed Finite Element Methods with Applications to Flow and Other Problems written by Max D. Gunzburger and published by . This book was released on 1983 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three problems were considered. These were finite element approximations due to the inhomogeneous Navier-Stokes equations, for potential flows, and for acoustic eigenvalue problems. In all cases both theoretical error estimates and computer codes implementing the best algorithm were developed. We also report on other activities sponsored by the grant, i.e. student research and conference talks.

Download or read book Mixed Finite Elements Compatibility Conditions and Applications written by Daniele Boffi and published by Springer Science & Business Media. This book was released on 2008-04-14 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

Download or read book A Comparison of Several Finite Element Methods to Solve the Stationary Navier Stokes Equations written by A. Segal and published by . This book was released on 1983 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book SIAM Journal on Scientific and Statistical Computing written by Society for Industrial and Applied Mathematics and published by . This book was released on 1988 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows written by Volker John and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The divergence constraint of the incompressible Navier-Stokes equations is revisited in the mixed finite element framework. While many stable and convergent mixed elements have been developed throughout the past four decades, most classical methods relax the divergence constraint and only enforce the condition discretely. As a result, these methods introduce a pressure-dependent consistency error which can potentially pollute the computed velocity. These methods are not robust in the sense that a contribution from the right-hand side, which in fluences only the pressure in the continuous equations, impacts both velocity and pressure in the discrete equations. This paper reviews the theory and practical implications of relaxing the divergence constraint. Several approaches for improving the discrete mass balance or even for computing divergence-free solutions will be discussed: grad-div stabilization, higher order mixed methods derived on the basis of an exact de Rham complex, H(div)-conforming finite elements, and mixed methods with an appropriate reconstruction of the test functions. Numerical examples illustrate both the potential effects of using non-robust discretizations and the improvements obtained by utilizing pressure-robust discretizations.