Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR‐C technique

By Juan José Ródenas, Manuel Tur, F. Fuenmayor, A. Vercher. 2007

83 citations recorded by the source corpus.

The superconvergent patch recovery (SPR) technique is widely used in the evaluation of a recovered stress field σ* from the finite element solution σfe. Several modifications of the original SPR technique have been proposed. A new improvement of the SPR technique, called SPR‐C technique (Constrained SPR), is presented in this paper. This new technique proposes the use of the appropriate constraint equations in order to obtain stress interpolation polynomials in the patch σ p* that locally satisfy the equations that should be satisfied by the exact solution. As a result the evaluated expressions for σ p* will satisfy the internal equilibrium and compatibility equations in the whole patch and the boundary equilibrium equation at least in vertex boundary nodes and, under certain circumstances, along the whole boundary of the patch coinciding with the boundary of the domain. The results show that the use of this technique considerably improves the accuracy of the recovered stress field σ* and therefore the local effectivity of the ZZ error estimator. Copyright © 2006 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/84771779aee5f09d7077af3672654a60287c5278

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Accurate recovery-based upper error bounds for the extended finite element framework (2010, methodology): “[31] proposes the use of the SPR-C technique [23] to obtain interpolation polynomials σi ⁎ that describe the recovered stress field in the patch of elements associated to each vertex node i.”
Efficient finite element methodology based on cartesian grids: application to structural shape optimization (2013, methodology): “In the proposed methodology, the recovery techniques developed by Ródenas and coworkers [39, 40, 42, 48] have been specially adapted both to be used in the Zienkiewicz and Zhu error estimator [34] that will guide the h-adaptive refinement process to improve the quality of the solution and to neutral”
A recovery‐type error estimator for the extended finite element method based on singular+smooth stress field splitting (2008, methodology): “This suggests the use of a method similar to that described in [34] in order to force the polynomials”
Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error (2007, methodology): “This is easily done by using the SPR-C technique [ 25 ], which is a modification of the standard SPR technique.”