A p‐hierarchical adaptive procedure for the scaled boundary finite element method
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This paper describes a p‐hierarchical adaptive procedure based on minimizing the classical energy norm for the scaled boundary finite element method. The reference solution, which is the solution of the fine mesh formed by uniformly refining the current mesh element‐wise one order higher, is used to represent the unknown exact solution. The optimum mesh is assumed to be obtained when each element contributes equally to the global error. The refinement criteria and the energy norm‐based error estimator are described and formulated for the scaled boundary finite element method. The effectivity index is derived and used to examine quality of the proposed error estimator. An algorithm for implementing the proposed p‐hierarchical adaptive procedure is developed. Numerical studies are performed on various bounded domain and unbounded domain problems. The results reflect a number of key points. Higher‐order elements are shown to be highly efficient. The effectivity index indicates that the proposed error estimator based on the classical energy norm works effectively and that the reference solution employed is a high‐quality approximation of the exact solution. The proposed p‐hierarchical adaptive strategy works efficiently. Copyright © 2007 John Wiley & Sons, Ltd.
Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/1421a547850d74cfa9d88da969a1fa79c347fbca
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In Computational Mechanics
In Electrical and Electronic Engineering
In Mechanics of Materials
Citations in the corpus
- A meshless local Petrov-Galerkin scaled boundary method (2005, methodology): “However, Deeks and Wolf [6] have shown that a uniform mesh performs very well when the scaled boundary finite-element method is used, as the singularity is modelled analytically.”
- Use of higher‐order shape functions in the scaled boundary finite element method (2006, methodology): “The method out-performs the finite element method when solving unbounded domain problems and problems involving stress singularities [7].”