Results 241 to 250 of about 539,151 (294)

Spectral, Spectral Element and Mortar Element Methods

2001
The spectral and spectral element discretizations of partial differential equations rely on high degree polynomial approximation and on the use of tensorized bases of polynomials. Firstly, on a square or a cube, we describe the basic tools for spectral methods, and we prove some optimal properties of polynomial approximation and interpolation. We apply
Christine Bernardi, Yvon Maday
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Spectral Finite Element Method

2018
In this chapter we describe a method to obtain the solution of second order linear differential equations by means of expansions into sets of Lagrange polynomials called discrete variable representation (DVR). The coefficients of the expansion are obtained by a Galerkin method.
George Rawitscher, Victo dos Santos Filho, Thiago Carvalho Peixoto   +2 more
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Spectral Element Methods on Simplicial Meshes

2013
We present a review in the construction of accurate and efficient multivariate polynomial approximations on elementary domains that are not Cartesian products of intervals, such as triangles and tetrahedra. After the generalities for high-order nodal interpolation of a function over an interval, we introduce collapsed coordinates and warped tensor ...
Rapetti, Francesca, Pasquetti, Richard
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Mimetic spectral element methods

AIP Conference Proceedings, 2015
Mimetic spectral element methods are arbitrary order methods which aim to mimic the underlying physical structure of a PDE. This is best accomplished in terms of differential geometry in which the physical variables are considered as differential k-forms. At the discrete level, the system is represented by k-cochains from algebraic topology.
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Spectral Finite Element Method

2011
This chapter presents the procedures for the development of various types of spectral elements. The chapter begins with basic outline of spectral finite element formulation and illustrates its utility for wave propagation studies is complex structural components.
Srinivasan Gopalakrishnan, Massimo Ruzzene, Sathyanarayana Hanagud   +2 more
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The Spectral Element Method

1997
We analyze the discretization of elliptic boundary-value problems defined in domains with a complicated shape, via a domain decomposition approach. The approximated solution is a patchwork of different algebraic polynomials defined in the subdomains and is determined as the result of a preconditioned iterative procedure.
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Overlapping Schwarz Methods for Unstructured Spectral Elements

Journal of Computational Physics, 2000
The authors introduce and study a parallel and scalable domain decomposition method for unstructured and hybrid spectral element discretizations of elliptic problems. The spectral elements are affine images of the reference triangle or square in two dimensions and of the reference tetrahedron, pyramid, prism, or cube in three dimensions.
L.F. Pavarino, T. Warburton
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Spectral Element Methods for Axisymmetric Stokes Problems

Journal of Computational Physics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gerritsma, M. I., Phillips, T. N.
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Dispersion Analysis for Discontinuous Spectral Element Methods

Journal of Scientific Computing, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stanescu, D., Kopriva, D. A., Hussaini, M. Y.   +2 more
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