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

Ainsworth, Mark and Allendes Flores, Alejandro Ignacio and Barrenechea, Gabriel and Rankin, Richard Andrew Robert (2013) On the adaptive selection of the parameter in stabilized finite element approximations. SIAM Journal on Numerical Analysis, 51 (3). pp. 1585-1609. ISSN 0036-1429

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    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