Journal ArticleDOI
Enhanced Superconvergent Patch Recovery incorporating equilibrium and boundary conditions
TLDR
In this paper, a patch recovery method based on superconvergent derivatives and equilibrium (SPRE), an enhancement of the SuperConvergent Patch Recovery (SPR), is studied for linear elasticity problems.Abstract:
Patch recovery based on superconvergent derivatives and equilibrium (SPRE), an enhancement of the Superconvergent Patch Recovery (SPR), is studied for linear elasticity problems. The paper also presents a further improvement for recovery of derivatives near boundaries, SPREB, where either tractions or displacements are prescribed. This is made by inclusion of weighted residual errors at boundary points in the patch recovery. A pronounced improvement in the post processed gradients of the finite element solution is observed by this method.read more
Citations
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Journal ArticleDOI
Recovery by Equilibrium in Patches (rep)
TL;DR: In this paper, a new recovery technique is developed, based on equilibrating the recovered stresses in the patch, in the same way that the standard FEM does, which leads to a weak form of equilibrium equations of new stresses on the patch and consequently to answers satisfying the discrete equilibrium conditions.
Journal ArticleDOI
Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery
Q. Z. Xiao,Bhushan Lal Karihaloo +1 more
TL;DR: In this paper, a statically admissible stress recovery (SAR) scheme is introduced to fit the stresses at sampling points (e.g. quadrature points) obtained by the extended/generalized finite element method (XFEM).
Journal ArticleDOI
Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 1: methodology and numerical procedure
TL;DR: In this article, a methodology for computing three-dimensional interaction between waves and fixed bodies is developed based on a fully non-linear potential flow theory, and the associated boundary value problem is solved using a finite element method (FEM).
Journal ArticleDOI
Error estimation and adaptivity for the finite element method in acoustics: 2D and 3D applications
TL;DR: In this article, two singularities inherent to the operator are demonstrated: the k-singularity, related to the phase shift between the exact and the numerical waves, and the λ -singularity corresponding to the singularity at the eigenfrequencies.
Journal ArticleDOI
Higher-Order Homogenization of Initial/Boundary-Value Problem
Jacob Fish,Wen Chen +1 more
TL;DR: In this paper, higher-order homogenization of an initial/boundary-value problem with oscillatory coefficients in one dimension is studied, and it is shown that higher terms are necessary to account for wave dispersion but introduce secular terms that grow unbounded in time.
References
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Journal ArticleDOI
Theory of Elasticity (3rd ed.)
Journal ArticleDOI
The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: In this article, a general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes, which has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems.
Journal ArticleDOI
The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: In this paper, the authors derived a theorem showing the dependence of the effectivity index for the Zienkiewicz-Zhu error estimator on the convergence rate of the recovered solution.
Journal ArticleDOI
Local and global smoothing of discontinuous finite element functions using a least squares method
E. Hinton,John S. Campbell +1 more
TL;DR: In this article, the concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced, and the relationship between local smoothing and the reduced integration technique is established.
Journal ArticleDOI
Optimal stress locations in finite element models
TL;DR: In this paper, the existence of optimal points for calculating accurate stresses within finite element models is discussed and a method for locating such points is proposed and applied to several popular finite elements.
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