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Saturday, August 1, 2020 | History

4 edition of Spectral element methods for the stokes problem found in the catalog.

Spectral element methods for the stokes problem

Cezary Niewiadomski

Spectral element methods for the stokes problem

by Cezary Niewiadomski

  • 394 Want to read
  • 19 Currently reading

Published by National Library of Canada in Ottawa .
Written in English


Edition Notes

Thesis (M.A.Sc.) -- University of Toronto, 2003.

SeriesCanadian theses = -- Thèses canadiennes
The Physical Object
FormatMicroform
Pagination2 microfiches : negative.
ID Numbers
Open LibraryOL20125163M
ISBN 100612782239
OCLC/WorldCa56329636

Introduction to finite and spectral element methods using MATLAB bending Hermite triangles Finite element methods for plate bending Viscous flow Stokes flow Navier-Stokes flow FINITE AND SPECTRAL ELEMENT METHODS IN THREE DIMENSIONS Convection-diffusion in three dimensions 4-node tetrahedral elements High-order and spectral tetrahedral. Abstract: Helps to understand both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. This work introduces the fundamentals and emphasizes algorithm development and computer implementation of the essential procedures.

Spectral / hp Element Methods for Computational Fluid Dynamics. 2nd ed. Oxford University Press, ISBN: Pozrikidis, Constantine. Introduction to Finite and Spectral Element Methods Using MATLAB. 2nd ed. Chapman and Hall / CRC, ISBN: [Preview with Google Books]. Plenty of books exist for finite difference and finite element methods, but there are fewer books on spectral methods. This is a self-contained presentation on the construction, implementation, and analysis of spectral methods for various differential and integral equations, with wide applications in science and engineering.

The spectral element method is a high-order finite element technique that combines the geometric flexibility of finite elements with the high accuracy of spectral methods. This method was pioneered in the mid 's by Anthony Patera at MIT and Yvon Maday at Paris-VI. Print book: Conference spectral element methods for large scale parallel Navier-Stokes calculations, P.F. Fisher and E.M. Ronquist, adaptive mesh strategies for the spectral element method, C. Mavriplis; hyperbolic equations, an essentially non-oscillatory reconstruction procedure on finite-element type meshes - application to compressible.


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Spectral element methods for the stokes problem by Cezary Niewiadomski Download PDF EPUB FB2

In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high degree piecewise polynomials as basis functions.

The spectral element method was introduced in a paper by A. Patera. Although Patera is credited with development of the method, his work. linear elasticity Stokes problem spectral element methods mixed methods preconditioned iterative methods substructuring Gauss-Lobatto-Legendre quadrature This work was supported by I.A.N-CNR, Pavia and by the National Science Foundation under Grant NSF-CCRCited by: 2.

Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains.

The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly.

In this paper we present a formulation of spectral vanishing viscosity (SVV) for the stabilisation of spectral/hp element methods applied to the solution of. () On the enforcement of the zero mean pressure condition in the spectral element approximation of the Stokes problem.

Computer Methods in Applied Mechanics and Engineering() Homogeneous and heterogeneous domain decomposition methods for plate bending by: Spectral Method Polynomial Approximation Discrete Problem Spectral Element Stokes Problem These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be updated as the learning algorithm by: 8. Description: This book is an essential reference for anyone interested in the use of spectral/hp element methods in fluid dynamics. It provides a comprehensive introduction to the field together with detailed examples of the methods to the incompressible and.

A numerical procedure is presented for solving the equations of Stokes flow past a fixed bed of rigid particles and the equations describing the motion of a suspension of rigid particles upon which a specified force and torque is exerted, for general Cited by: In Section 4, we put forward a new triangular spectral-element method for the modal elliptic problem; we present the approximation scheme, the analysis of convergence and do three tests.

In Section 5, we implement this TSEM to the steady Stokes : Jingliang Li, Jingliang Li, Heping Ma, Huiyuan Li. Mortar Spectral Element Discretization of the Stokes Problem in Axisymmetric Domains Article in Numerical Methods for Partial Differential Equations 30(1) January with 86 Reads.

We present a procedure to enhance the accuracy of spectral element methods for the evolutionary Navier--Stokes equations. The approximations to the velocity and the pressure obtained using a spectr Cited by: Spectral Element Method in Structural Dynamics is a concise and timely introduction to the spectral element method (SEM) as a means of solving problems in structural dynamics, wave propagations, and other related fields.

The book consists of three key sections. In the first part, background knowledge is set up for the readers by reviewing previous work in the area and by Cited by: Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method.

There was a problem filtering reviews right now. Please try again later. out of 5 stars Five /5(2). Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, potentially involving the use of the fast Fourier idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and then to choose.

An excellent source on spectral finite elements (includes code) is the recent book by Pozrikidis: Introduction to Finite and Spectral Element Methods using MATLAB (snippets from the chapters).

The style and content is aligned with that of a textbook and not a research monograph. It provides a very nice transition from finite elements to spectral. 2 Spatialdiscretizationofpartialdi erentialequa-tions Introduction Finitevolume, niteelement,spectralandalso nitedi erencemethodsmaybeviewed.

The reader is referred to the book by Deville et al., chapters 3 and 6, for an extensive treatment of this issue in the spectral-element framework. 6 Sem Versus Analytic Solutions: Steady and Unsteady Stokes ProblemsCited by: Legendre-Laguerre spectral-element method for the Stokes problems in a simple geome-try, for the sake of the clarity.

It is evident that this analysis can be extended to complex geometries by using standard arguments of the spectral-element method. The outline of this paper is as follows. In Sect. 2 we present the Stokes problem in a semi. Navier-Stokes are introduced in the context of the spectral and finite element methods.

Some results ofthe practical implementation of SEM to 2-D problems are presented. KeywordsCited by: The Stokes equations are solved using spectral methods with staggered and nonstaggered grids. Numerous ways to avoid the problem of spurious pressure modes are presented, including new techniques using the pseudospectrdJ method and a method solving the weak.

Though some FSE methods have been presented in [25, 26], as far as we know, there has not been any report that the Crank–Nicolson (CN) finite spectral element (CNFSE) method is used to solve the 2D non-stationary Stokes equations about vorticity–stream functions, especially, there has not been any report about the theoretical analysis of Cited by: 1.So, this paper is aimed to the a posteriori analysis of the penalized spectral element discretization of the Stokes problem.

Numerical experiments confirm the interest of such an algorithm and also allow us to compare the cases of discretizations with optimal or non optimal inf-sup constants.

An outline of the paper is as by: 3.Spectral/hp element methods for CFD George Em Karniadakis, Spencer J. Sherwin Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational .