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On Higher Order Pyramidal Finite Elements
Advances in Applied Mathematics and Mechanics, 2011AbstractIn this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials.
Liu, L. +3 more
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Higher-order finite elements for embedded simulation
ACM Transactions on Graphics, 2020As demands for high-fidelity physics-based animations increase, the need for accurate methods for simulating deformable solids grows. While higherorder finite elements are commonplace in engineering due to their superior approximation properties for many problems, they have gained little traction in the computer graphics community.
Andreas Longva +4 more
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Higher-Order Finite Element for Sandwich Plates
AIAA Journal, 1998A finite element model for the analysis of sandwich plates with laminated composites face-sheets is developed. In the model, the face-sheets are represented as ReissnerMindlin plates and therefore include shear deformation effects. The core is modelled as a three-dimensional continuum in which the through-thickness representation of the displacement ...
S. Oskooei, J. S. Hansen
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Electromagnetic Scattering by Isoparametric Elements of Higher Order
Computational Methods in Applied Mathematics, 2014Abstract. A boundary element method with higher order isoparametric elements allows for the simulation of scattering problems given by the electric field integral equation. This paper describes the implementation and provides striking numerical evidence of the higher order convergence rates for the approximation of the electric surface ...
Lucy Weggler +2 more
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Local Approach to Higher-Order Contact Elements
Reports on Mathematical Physics, 2006Let \(N\) be an \(n\)-dimensional submanifold of an \(m\)-dimensional manifold \(M\). In this paper, the author defines regular \(n\)-dimensional velocities of order \(r\) and \(n\)-dimensional contact elements of order \(r\) determined by \(N\) and presents their local descriptions.
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