On the adaptive selection of the parameter in stabilized finite element approximations

@article{aaa7d9f471764c7fb225b66b68349aca,

title = “On the adaptive selection of the parameter in stabilized finite element approximations”,

abstract = “A systematic approach is developed for the selection of the stabilization parameter for stabilized finite element approximation of the Stokes problem, whereby the parameter is chosen to minimize a computable upper bound for the error in the approximation. The approach is applied in the context of both a single fixed mesh and an adaptive mesh refinement procedure. The optimization is carried out by a derivative-free optimization algorithm and is based on minimizing a new fully computable error estimator. Numerical results are presented illustrating the theory and the performance of the estimator, together with the optimization algorithm.”,

keywords = “Computable error bounds, Derivative-free optimization, Stabilization parameter, Stabilized finite element method”,

author = “Mark Ainsworth and Alejandro Allendes and Barrenechea, {Gabriel R.} and Richard Rankin”,

year = “2013”,

doi = “10.1137/110837796”,

language = “English”,

volume = “51”,

pages = “1585–1609”,

journal = “SIAM Journal on Numerical Analysis”,

issn = “0036-1429”,

publisher = “Society for Industrial and Applied Mathematics Publications”,

number = “3”,

}