Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery

in Computational Mechanics (2013)

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for ... [more ▼]

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems). These GOEE are one of the key unsolved problems of advanced engineering applications in, for example, the aerospace industry. This work presents a simple recovery-based error estimation technique for QoIs whose main characteristic is the use of an enhanced version of the Superconvergent Patch Recovery (SPR) technique previously used for error estimation in the energy norm. This enhanced SPR technique is used to recover both the primal and dual solutions. It provides a nearly statically admissible stress field that results in accurate estimations of the local contributions to the discretisation error in the QoI and, therefore, in an accurate estimation of this magnitude. This approach leads to a technique with a reasonable computational cost that could easily be implemented into already available finite element codes, or as an independent postprocessing tool. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

Error estimation of recovered solutions in FE analysis. Higher order h-adaptive refinement strategies

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

Error estimation and bounding in energy norm based on a displacement recovery technique

in Eberhardsteiner, Josef; Böhm, Helmut; Rammerstorfer, F G (Eds.) 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) (2012)

Error estimation and error bounding in energy norm based on a displacement recovery technique

in ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (2012)

Traditionally, recovery based error estimators in linear elasticity have considered the evaluation of an enhanced stress field obtained from the raw Finite Element (FE) stress solution. Instead of that ... [more ▼]

Traditionally, recovery based error estimators in linear elasticity have considered the evaluation of an enhanced stress field obtained from the raw Finite Element (FE) stress solution. Instead of that, one can also obtain a recovered displacement field from the FE displacements. Herein, we describe a superconvergent patch recovery of the displacement field which considers the local fulfilment of boundary and internal equilibrium equations, Dirichlet constraints and, for singular problems, the splitting of the displacement and stress fields into singular and smooth parts. Numerical tests using problems with known analytical solution have been carried out to validate the proposed technique for error estimation and error bounding in energy norm and quantities of interest. [less ▲]

Comparison of recently developed recovery type discretization error estimators for the extended finite element method

in Schrefler, B A; Perego, U (Eds.) 8th World Congress on Computational Mechanics (WCCM8). 5th.European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) (2008)