New bounding techniques for goal-oriented error estimation applied to linear problems
For computational scientists using finite element methods, this provides more accurate and guaranteed error estimates for linear problems, though it is an incremental improvement over existing bounding techniques.
The paper introduces new bounding techniques based on Saint-Venant's principle and homothetic domains to improve guaranteed error bounds for outputs of interest in linear finite element problems, achieving more accurate boundings of local error contributions.
The paper deals with the accuracy of guaranteed error bounds on outputs of interest computed from approximate methods such as the finite element method. A considerable improvement is introduced for linear problems thanks to new bounding techniques based on Saint-Venant's principle. The main breakthrough of these optimized bounding techniques is the use of properties of homothetic domains which enables to cleverly derive guaranteed and accurate boundings of contributions to the global error estimate over a local region of the domain. Performances of these techniques are illustrated through several numerical experiments.