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Higher-Order Elements

1999
In the earlier seven chapters, we solved by the Green element method a variety of engineering problems in 1-D. spatial dimensions ranging from steady to transient, linear to nonlinear, and from those which apply in homogeneous to heterogeneous media.
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Asteroid Mean Elements: Higher Order and Iterative Theories

Celestial Mechanics and Dynamical Astronomy, 1998
The authors present an accurate and reliable algorithm to compute mean elements of asteroids. A satisfactory accurracy is obtained much closer to the strongest mean motion resonances. The fixed-point-based algorithm is iterative, with the first-order theory as an iteration step.
MILANI COMPARETTI, ANDREA   +1 more
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Methods and framework for visualizing higher-order finite elements

IEEE Transactions on Visualization and Computer Graphics, 2006
The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain.
William J. Schroeder   +6 more
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Locations of optimal stress points in higher‐order elements

Communications in Numerical Methods in Engineering, 1999
Summary: The locations of optimal stress points in Lagrangian and serendipity elements are determined by using the symbolic mathematical tool MATHEMATICA. It is found that, for the Lagrange family of elements of order more than two, the coordinates of optimal stress points slightly differ from those of the reduced Gauss integration points.
Oh, Hyung-Seok, Batra, R. C.
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Higher Order Finite Element Methods

2017
The efficiency of numerical methods for wave propagation analysis is essential, as very fine spatial and temporal resolutions are required in order to properly describe all the phenomena of interest, such as scattering, reflection, mode conversion, and many more.
S. Duczek, C. Willberg, U. Gabbert
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Synthetic circuit elements of higher order with current conveyors

Asia-Pacific Conference on Circuits and Systems, 2003
The design of a synthetic element of higher-order immittance function using transformation circuits is described. A new current conveyor structure for low x-terminal input impedance has been used and its model has been presented. PSpice simulation of a third-order Chebyshev lowpass filter is included.
Ivo Lattenberg   +3 more
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Higher order finite element analysis of lake circulation

Computers & Fluids, 1973
Abstract The finite element method is applied to the analysis of the wind-driven circulation of variable-depth, shallow, homogenous lakes. Attention is concentrated upon higher-order description of the flow phenomena within the individual elements and upon the use of these higher order functions in the definition of curved element boundaries ...
Gallagher, Richard H.   +1 more
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A higher‐order triangular plate bending element revisited

International Journal for Numerical Methods in Engineering, 1990
AbstractA new formulation of an eighteen‐degrees‐of‐freedom higher‐order triangular plate bending element using triangular area co‐ordinates is presented. The displacement function w is taken as the complete fifth‐order polynomial in area co‐ordinates. The normal slope along an edge of the triangle is constrained to vary cubically.
Dasgupta, Suman, Sengupta, Dipak
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A novel approach for devising higher‐order hybrid elements

International Journal for Numerical Methods in Engineering, 1993
AbstractThis paper presents an efficient way to devise higher‐order hybrid elements by generalizing the admissible matrix formulation recently proposed by the author. The assumed stress or strain is first decomposed into the constant, lower‐ and higher‐order modes.
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Two-Dimensional Higher Order Elements

2014
The triangular elements with quadratic and cubic shape functions in terms of the local area coordinates are presented and coordinate transformation law with the associated Jacobian matrix calculations are given in the chapter. As an application, the Field problem in two dimensions is considered and employing the quadratic triangular element, the ...
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