Stabilized nonconforming finite element methods for data assimilation in incompressible flows
arXiv:1609.0604411 citations
Originality Synthesis-oriented
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Provides a theoretically grounded numerical method for assimilating nonstandard data in incompressible flows, relevant to computational fluid dynamics and inverse problems.
The authors develop a stabilized nonconforming finite element method for data assimilation in Stokes flows, achieving optimal error estimates relative to the ill-posed problem's conditional stability.
We consider a stabilized nonconforming finite element method for data assimilation in incompressible flow subject to the Stokes' equations. The method uses a primal dual structure that allows for the inclusion of nonstandard data. Error estimates are obtained that are optimal compared to the conditional stability of the ill-posed data assimilation problem.