Abstract
The paper is concerned with the formulation of recovery-based a posteriori error estimators. At first we analyze a variant of the well-known Zienkiewicz-Zhu method, which is here formulated so as to be exact in one dimension for quadratic solutions on non-uniform grids. Next, we discuss two methods which operate directly on the solution, rather than its gradient: one is based on a solution enrichment using the Zienkiewicz-Zhu recovered gradient, while the other consists of a roughening of the solution followed by a Zienkiewicz-Zhu-like recovery. The three new proposed methods are compared in terms of their effectivity indices and solution accuracy to the Zienkiewicz-Zhu estimator, and are applied to representative two- and three-dimensional problems.
Original language | English |
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Pages (from-to) | 4794-4815 |
Number of pages | 22 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 195 |
Issue number | 37-40 |
DOIs | |
State | Published - 15 Jul 2006 |
Externally published | Yes |
Keywords
- A posteriori analysis
- Error estimators
- Finite elements
- Recovery techniques