A local projection stabilized method for fictitious domains

Barrenechea, Gabriel R. and Chouly, Franz (2012) A local projection stabilized method for fictitious domains. Applied Mathematics Letters, 25 (12). pp. 2071-2076. ISSN 0893-9659 (https://doi.org/10.1016/j.aml.2012.04.020)

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In this work a local projection stabilization method is proposed for solving a fictitious domain problem. The method adds a suitable fluctuation term to the formulation, thus yielding the natural space for the Lagrange multiplier stable. Stability and convergence are proved and these results are illustrated with a numerical experiment.