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Wednesday, July 8, 2020 | History

4 edition of Nonlinear elliptic and evolution problems and their finite element approximations found in the catalog.

Nonlinear elliptic and evolution problems and their finite element approximations

by A ЕЅenГ­ЕЎek

  • 104 Want to read
  • 28 Currently reading

Published by Academic Press in London, San Diego, CA .
Written in English

    Subjects:
  • Finite element method,
  • Nonlinear theories

  • Edition Notes

    StatementA. Ženíšek ; translation editor, J.R. Whiteman
    SeriesComputational mathematics and applications, Computational mathematics and applications
    ContributionsWhiteman, J. R.
    The Physical Object
    Paginationxix, 422 p. ;
    Number of Pages422
    ID Numbers
    Open LibraryOL16695347M
    ISBN 10012779560X

    FINITE ELEMENT APPROXIMATION AND ITERATIVE SOLUTION OF A CLASS OF MILDLY NON-LINEAR ELLIPTIC EQUATIONS Tony CHAN* Computer Science Department Stanford University Serra House, Serra Street Stanford, California and WC Roland GLOWINSKI Universitg Pierre et Marie Curie Analyse Num6rique L.A. 4, Place Jussieu Paris Cedex Abstract: We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (, SISC) allowing us to work directly on the strong form of a linear by: 1.

    Nonlinear Elliptic and Evolution Problems and their Finite Element Approximation, (). Numerical Analysis of a Coupled Pair of CahnHilliard Equations,Author: Abdalaziz Saleem Al-Ofl. A. Ženíšek, "Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations,", Computational Mathematics and Applications. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (). Google Scholar [31] Alexander Ženíšek, Finite element methods for coupled thermoelasticity and coupled consolidation of clay Cited by:

    On Their Approximation 1 Introduction An important and very useful class of non-linear problems arising from 1 mechanics, physics etc. consists of the so-called Variational Inequali-ties. We mainly consider the following two types of variational inequal-ities, namely 1. Elliptic Variational Inequalities (EVI), 2. Parabolic Variational. We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as Cited by:


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Nonlinear elliptic and evolution problems and their finite element approximations by A ЕЅenГ­ЕЎek Download PDF EPUB FB2

The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function : Birkhäuser Basel.

We present a Galerkin method with piecewise polynomial continuous elements for fully nonlinear elliptic equations. A key tool is the discretization proposed in Lakkis and Pryer,allowing us to work directly on the strong form of a linear PDE.

An added benefit to making use of this discretization method is that a recovered (finite element) Hessianis a byproduct of the solution by: Finite element approximations and non-linear relaxation, augmented Lagrangians, and nonlinear least square methods are all covered in detail, as are many applications.

"Numerical Methods for Nonlinear Variational Problems", originally published in the Springer Series in Computational Physics, is a classic in applied mathematics and Brand: Springer-Verlag Berlin Heidelberg.

This book presents the advances in developing elliptic problem solvers and analyzes their performance. Organized into 40 chapters, this book begins with an overview of the approximate solution of using a standard Galerkin method employing piecewise linear triangular finite elements.

A. Ženíšek: Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations. Academic Press, London, Academic Press, London, Google ScholarAuthor: Jana Zlamalova. concerning the properties and numerical solution of problems with disconti-nuous coefficients can be found e.g.

in [1, 13, 20, 21, 22]. In this paper we present a gênerai theory of the finite element solution to nonlinear équation () with discontinuous coefficients in a bounded domain Ci c= R2.

We generalize hère the methods and Cited by: The book contains the study of convex fully nonlinear equations and fully nonlinear equations with variable coefficients. This book is suitable as a text for graduate courses in nonlinear elliptic.

Mixed finite element methods are developed to approximate the solution of the Dirichlet problem for the most general quasi-linear second-order elliptic operator in divergence form.

Existence and un. MULTISCALE FINITE ELEMENT METHODS FOR NONLINEAR PROBLEMS AND THEIR APPLICATIONS Y. EFENDIEV, T. HOUy, AND V. GINTINGz Abstract. In this paper we propose a generalization of multiscale nite element methods (MsFEM) to nonlinear problems. We study the convergence of the proposed method for nonlinear elliptic equations and propose an oversampling File Size: KB.

obtain a good approximation of some function of the gradient of the solution of the differential equation (which may represent, for example, a velocity field. or electric field) as an approximation of the solution itself (which may repre- sent, respectively, a pressure or an electric potential).

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, creating an exciting interplay between the subjects. This is the first and only book to prove in a systematic and unifying way, stability, convergence and computing results for the different numerical methods for nonlinear elliptic by: Nonlinear elliptic boundary value problems versus their finite difference approximations: numerically irrelevant Solutions*) By H.

Peitgen and D. Saupe at Bremen and K. Schmitt at Salt Lake City 1. Introduction The aim of this paper is to continue and extend the discussion in [9] concerning the. Additional Physical Format: Online version: Ženíšek, A.

Nonlinear elliptic and evolution problems and their finite element approximations. London ; San Diego: Academic Press, © Elliptic Problem Solvers, II covers the proceedings of the Elliptic Problem Solvers Conference, held at the Naval Postgraduate School in Monterey, California from January 10 to 12, The book focuses on various aspects of the numerical solution of elliptic boundary value problems.

Purchase The Finite Element Method for Elliptic Problems, Volume 4 - 1st Edition. Print Book & E-Book. ISBNPages: Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, creating an exciting interplay between the subjects.

This is the first and only book to prove in a systematic and unifying way, stability, convergence and computing results for the different numerical methods for nonlinear elliptic problems. Accordingly this book is primarily intended for mathematicians working in the field of elliptic partial differential equations as well as for numerical analysts and users of such elliptic equations.

The computation of nonlinear quasistationary two-dimensional magnetic fields leads to a nonlinear second order parabolic-elliptic initial-boundary value problem. Such a problem with a nonhomogeneous Dirichlet boundary condition on a part Γ1 of the boundary is studied in this paper.

The problem is discretized in space by the finite element method with linear functions on triangular elements Author: Dana Říhová-Škabrahová. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): recently showed that mixed variational problems, and their numerical approximation by mixed methods, could be most completely understood using the ideas and tools of Hilbert complexes.

This led to the development of the Finite Element Exterior Calculus (FEEC) for a large class of linear elliptic problems. Arnold, Falk, and Winther [Bull. Amer. Math. Soc. 47 (), ] showed that mixed variational problems, and their numerical approximation by mixed methods, could be most completely understood using the ideas and tools of Hilbert complexes.

This led to the development of the Finite Element Exterior Calculus (FEEC) for a large class of linear elliptic problems. More recently, Holst and Cited by: 1. Abstract: Arnold, Falk, and Winther [Bull. Amer. Math. Soc. 47 (), ] showed that mixed variational problems, and their numerical approximation by mixed methods, could be most completely understood using the ideas and tools of Hilbert complexes.

This led to the development of the Finite Element Exterior Calculus (FEEC) for a large class of linear elliptic by: 1.through all elements and their faces.

In §§ we apply the general results of the previous sections to finite ele-ment approximations of scalar quasi-linear elliptic partial differential equations of 2nd order, the eigenvalue problem for scalar linear elliptic differential oper.Adaptive finite element methods for a class of evolution problems in viscoplasticity 2.

The nonelastic strain rate is a function of the stress and a set of internal-state-variables where d is the stress tensor, and Zt is a set of state variables which may be tensors and/or scalars. 3.