r4.10.06 Error estimators in quantities of interest

Summary:

In this document, the framework for estimating error in quantity of interest is presented. This framework is used with explicit residue estimators as well as with smoothing estimators. A number of quantities of interest are detailed, in particular their writing in terms of loading for the dual problem.

Table of Contents

• 1. Problem model and notations
  • 1.1. Equations
  • 1.2. Variational formulation
  • 1.3. Finite element discretization
  • 1.4. Discretization error
  • 1.5. A priory error estimation
• 2. Posterior error estimators
  • 2.1. Definition of a posteriori estimators
  • 2.2. Quality of estimators
• 3. Local error
  • 3.1. Pollution error
  • 3.2. Error in quantity of interest
• 4. Estimation of the error in quantity of interest
  • 4.1. Quantity-of-interest error estimator based on explicit residuals
  • 4.2. Quantity of interest estimator based on field smoothing
  • 4.3. Estimator in quantity of interest based on hierarchical bases
• 5. Formulation of the quantity of interest
  • 5.1. Quantities associated with travel
  • 5.2. Quantities associated with constraints
  • 5.3. Quantities related to fracture mechanics
• 6. Implementation and use in Code_Aster
• 7. Bibliography
• 8. Description of document versions