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Wednesday, October 14, 2020 | History

3 edition of Optimal least-squares finite element method for elliptic problems found in the catalog.

Optimal least-squares finite element method for elliptic problems

Optimal least-squares finite element method for elliptic problems

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  • 32 Currently reading

Published by National Aeronautics and Space Administration, For sale by the National Technical Information Service in [Washington, DC], [Springfield, Va .
Written in English

    Subjects:
  • Finite element method.,
  • Least squares.

  • Edition Notes

    Other titlesOptimal least squares finite element ....
    StatementBo-Nan Jiang and Louis A. Povinelli.
    SeriesNASA technical memorandum -- 105382, ICOMP -- 91-29
    ContributionsPovinelli, Louis A., United States. National Aeronautics and Space Administration.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL17104067M

    CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. First-order system least squares (FOSLS) is a recently developed methodology for solving partial differential equations. Among its advantages are that the finite element spaces are not restricted by the inf-sup condition imposed, for example, on mixed methods and that the least-squares functional itself. In this paper, a few dual least‐squares finite element methods and their application to scalar linear hyperbolic problems are studied. The purpose is to obtain L 2 ‐norm approximations on finite element spaces of the exact solutions to hyperbolic partial differential equations of interest.

    \The Finite Element Method: Linear Static and Dynamic Finite Element Analysis", by T. J. R. Hughes, Dover Publications, class of methods. More speci cally, Elliptic equations are most commonly associated with a di usive or (Galerkin, Collocation, Least Squares methods, etc) Visit our Course page on Linear FEM for further details. Some types of finite element methods (conforming, nonconforming, mixed finite element methods) are particular cases of the gradient discretization method (GDM). Hence the convergence properties of the GDM, which are established for a series of problems (linear and non-linear elliptic problems, linear, nonlinear, and degenerate parabolic.

    On the other hand, the least squares finite element method is ideally suited for non-linear problems regardless of the nature of equations and the nature of the nonlinearities. In this paper the authors investigate the competitiveness of the p-version least square finite more» element formulation (LSFEF) and p-version Galerkin method for non. Abstract Theory of Least-Squares Finite Element Methods. Mathematical Foundations. First-Order Agmon-Douglis-Nirenberg Systems --Part III. Least-Squares Methods for Elliptic Problems. Basic First-Order Systems. Application to Key Elliptic Problems --Part IV. Extensions of Least-Squares Methods to other Problems. The Navier-Stokes Equations.


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Optimal least-squares finite element method for elliptic problems Download PDF EPUB FB2

ABSTRACT (Maximum words) In this paper, we propose an optimal least-squares finite element method for 2D and 3D elliptic problems and discuss its advantages over the mixed Galerkin method and the usual least-squares finite element method.

Purchase The Finite Element Method for Elliptic Problems, Volume 4 - 1st Edition. Print Book & E-Book. ISBNPages: The Finite Element Method for Elliptic Problems is the only book available that analyzes in depth the mathematical foundations of the finite element method.

It is a valuable reference and introduction to current research on the numerical analysis of the finite element method, as well as a working textbook for graduate courses in numerical analysis. It includes many useful figures, and there are many.

Preliminaries and notation In this paper, we present the essential idea of the optimal least-squares finite element method by solving the following second-order elliptic boundary-value problem: V. Vu + u = f(x) inf/, Vu " n -'- g(x) on F, (1) where/2 C R" (n = 2 or 3) is an open bounded convex domain with a piecewise C~ boundary F, x--(x~, x, x3) is a point in n, n = (rim, n2, n.~) is a unit outward Cited by: This book is valuable both for researchers and practitioners working in least-squares finite element methods.

In addition, others will find it a great reference for learning about the theory and implementation of the least-squares finite element methods.” (Tsu Cited by: Also included are recent advances such as compatible LSFEMs, negative-norm LSFEMs, and LSFEMs for optimal control and design problems.

Numerical examples illustrate key aspects of the theory ranging from the importance of norm-equivalence to connections between compatible LSFEMs and classical-Galerkin and mixed-Galerkin methods.

Gunzburger and H.-C. Lee; A penalty/least-squares method for optimal control problems for first-order elliptic systems, Appl. Math. Comp. P. Bochev and M. Gunzburger; Least-squares finite element methods for optimization and control problems for the Stokes equations, Comp. Math.

Appl. 48Least-squares finite element methods are an attractive class of methods for the numerical solution of partial differential equations. They are motivated by the desire to recover, in general. The Compatible Least-Squares Finite Element Method with a Reaction Term The Compatible Least-Squares Finite Element Method Without a Reaction Term Practicality Issues Practical Rewards of Compatibility Compatible Least-Squares Finite Element Methods on Non-Affine Grids FINITE ELEMENT METHODS FOR ELLIPTIC PROBLEMS 1 Amiya Kumar Pani Industrial Mathematics Group Department of Mathematics Indian Institute of Technology, Bombay Powai, Mumbai 76 (India).

IIT Bombay, March 1Workshop on ‘Mathematical Foundation of Advanced Finite Element Methods (MFAFEM) held in BITS,GOA during 26th December - 3rd. The least-squares finite element method applied to the 3 x 3 linear system will not be convergent without other restrictions.

For overcoming this shortcoming, we add an equation curl u = 0 to the system (), as divu+k2~b=f inJ~, curl u in J2, V~ - u = O inn, () uXn=O onE.

C.L. Chang, A least-squares FEM for the Helmholtz equation 3 It is a system with 3 variables and 4 equations. Guo H, Fu H and Zhang J () A splitting positive definite mixed finite element method for elliptic optimal control problem, Applied Mathematics and Computation,(), Online publication date: 1-Aug A SPLITTING LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS HONGFEI FU, HONGXING RUI1, HUI GUO, JIANSONG ZHANG, AND JIAN HOU Abstract.

In this paper, we propose a splitting least-squares mixed finite element method for the approximation of elliptic optimal control problem with the control constrained by pointwise.

Efficient numerical methods for solving Poisson equation constraint optimal control problems with random coefficient are discussed in this paper.

By applying the finite element method and the Monte Carlo approximation, the original optimal control problem is discretized and transformed into an optimization problem. Get this from a library.

Optimal least-squares finite element method for elliptic problems. [Bo-Nan Jiang; Louis A Povinelli; United States. National Aeronautics and Space Administration.].

Abstract. Over the last decades the finite element method, which was introduced by engineers in the s, has become the perhaps most important numerical method for partial differential equations, particularly for equations of elliptic and parabolic method is based on the variational form of the boundary value problem and approximates the exact solution by a piecewise polynomial.

The Finite Element Method for Elliptic Problems is the only book available that fully analyzes the mathematical foundations of the finite element method. It is a valuable reference and introduction to current research on the numerical analysis of the finite element method, and also a working textbook for graduate courses in numerical analysis.3/5(1).

Least-Squares Finite Element Methods | Pavel B. Bochev, Max D. Gunzburger | download | B–OK. Download books for free.

Find books. The presented adaptive algorithm for Raviart-Thomas mixed finite element methods solves the Poisson model problem, with optimal convergence rate. Discover the world's research 17+ million members. This book is valuable both for researchers and practitioners working in least-squares finite element methods.

In addition, others will find it a great reference for learning about the theory and implementation of the least-squares finite element methods.” (Tsu. A splitting positive definite mixed finite element method for elliptic optimal control problems.

Appl. Math. Comput.() Google Scholar Digital Library; Hughes, T., Franca, L.P., Hulbert, G.: A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advectivediffusive.The finite element method for elliptic problems / Philippe G.

Ciarlet North-Holland Pub. Co. ; sole distributors for the U.S.A. and Canada, Elsevier North-Holland Amsterdam ; New York: New York Australian/Harvard Citation.() A discontinuous Galerkin Method for parabolic problems with modified hp-finite element approximation technique.

Applied Mathematics and Computation() Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem.