Superconvergent patch recovery technique for the finite element method in acoustics

Abstract

A posteriori error estimation has become very popular, mainly in linear elasticity. A robust implementation of the superconvergent patch recovery technique of 0. C. Zienkiewicz and J. Z. Zhu is presented for acoustic finite element analyses: the original concepts are extended to complex variables, and both local and global behaviours of the recovery procedure and the error estimation are studied. The numerical tests confirm the improvement of the rates of convergence for the recovered solution and also show the reliability of the error estimator except at frequencies corresponding either to the analytical or to the finite element eigenfrequencies.

Strategies involving the local defect correction multi-level refinement method for solving three-dimensional linear elastic problems

“…We decided to use the Zienkiewicz and Zhu (ZZ) a posteriori error estimator [40]. This is the most commonly used a posteriori error estimator (see for example [34,[67][68][69][70]), and its super-convergent patch recovery version [71,72] gives excellent performances in terms of its accuracy versus time consumption. In addition, it is easy to use and is already available in some industrial codes, as Code_Aster [73] or CAST3M [64].…”