Results 81 to 90 of about 3,208 (179)
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2012
In this chapter we study the concept of a finite element in some more detail. We begin with the classical definition of a finite element as the triplet of a polygon, a polynomial space, and a set of functionals. We then show how to derive shape functions for the most common Lagrange elements.
Mats G. Larson, Fredrik Bengzon
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In this chapter we study the concept of a finite element in some more detail. We begin with the classical definition of a finite element as the triplet of a polygon, a polynomial space, and a set of functionals. We then show how to derive shape functions for the most common Lagrange elements.
Mats G. Larson, Fredrik Bengzon
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SIAM Journal on Numerical Analysis, 1972
This paper considers matrices arising from the use of finite element techniques in least-squares approximation and in elliptic partial differential equations; it studies their properties of numerical stability, and in particular, it establishes bounds for their inverses with respect to the uniform norm.
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This paper considers matrices arising from the use of finite element techniques in least-squares approximation and in elliptic partial differential equations; it studies their properties of numerical stability, and in particular, it establishes bounds for their inverses with respect to the uniform norm.
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Probabilistic finite element analysis of a craniofacial finite element model
Journal of Theoretical Biology, 2012We employed a probabilistic finite element analysis (FEA) method to determine how variability in material property values affects stress and strain values in a finite model of a Macaca fascicularis cranium. The material behavior of cortical bone varied in three ways: isotropic homogeneous, isotropic non-homogeneous, and orthotropic non-homogeneous. The
David S. Strait +6 more
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2002
The finite-difference approach with equidistant grids is easy to understand and straightforward to implement. The resulting uniform rectangular grids are comfortable, but in many applications not flexible enough. Steep gradients of the solution require a finer grid such that the difference quotients provide good approximations of the differentials.
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The finite-difference approach with equidistant grids is easy to understand and straightforward to implement. The resulting uniform rectangular grids are comfortable, but in many applications not flexible enough. Steep gradients of the solution require a finer grid such that the difference quotients provide good approximations of the differentials.
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1970
In this chapter the principles of the finite element method will be presented through the application to problems of steady and nonsteady groundwater flow. The method was developed in the 1950’s, first for problems of aeronautical engineering (the construction of airplanes), mechanical engineering (nuclear reactor vessels), and civil engineering ...
Jacob Bear, Arnold Verruijt
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In this chapter the principles of the finite element method will be presented through the application to problems of steady and nonsteady groundwater flow. The method was developed in the 1950’s, first for problems of aeronautical engineering (the construction of airplanes), mechanical engineering (nuclear reactor vessels), and civil engineering ...
Jacob Bear, Arnold Verruijt
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Computers & Structures, 1979
Abstract This paper describes an extension to the classical finite element analysis methods. Using the same data inherent in the stiffness matrix, and adding cost parameters as input, a finite element structural analysis program is shown to output cost data.
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Abstract This paper describes an extension to the classical finite element analysis methods. Using the same data inherent in the stiffness matrix, and adding cost parameters as input, a finite element structural analysis program is shown to output cost data.
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1991
The approximate methods presented at the end of the preceding chapter for the solution of the vibration problems of continuous systems are based on the assumption that the shape of the deformation of the continuous system can be described by a set of assumed functions. By using this approach, the vibration of the continuous system which has an infinite
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The approximate methods presented at the end of the preceding chapter for the solution of the vibration problems of continuous systems are based on the assumption that the shape of the deformation of the continuous system can be described by a set of assumed functions. By using this approach, the vibration of the continuous system which has an infinite
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1992
Die mathematische Behandlung der Finite-Element-Verfahren fust auf der Variationsformulierung elliptischer Differentialgleichungen. Die Losungen der wichtigsten Differentialgleichungen lassen sich durch Minimaleigenschaften charakterisieren. Die Variationsaufgaben besitzen Losungen in den Funktionenraumen, die man als Sobolev-Raume bezeichnet.
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Die mathematische Behandlung der Finite-Element-Verfahren fust auf der Variationsformulierung elliptischer Differentialgleichungen. Die Losungen der wichtigsten Differentialgleichungen lassen sich durch Minimaleigenschaften charakterisieren. Die Variationsaufgaben besitzen Losungen in den Funktionenraumen, die man als Sobolev-Raume bezeichnet.
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Elements of finite element programming
2014In this chapter we focus more deeply on a number of aspects relating to the translation of the finite-element method into computer code. This implementation process can hide some pitfalls. Beyond the syntactic requirements of a given programming language, the need for a high computational efficiency leads to an implementation that is generally not the ...
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Finite Differences and Finite Elements
2011In the preceding chapters, we have described the numerical solution techniques most commonly applied in ocean-acoustic propagation modeling. One or more of these approaches are numerically efficient for the majority of forward problems occurring in underwater acoustics, including propagation over very long ranges, with or without lateral variations in ...
Michael B. Porter +3 more
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