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A penalty-free Shifted Boundary Method of arbitrary order

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arxiv 2306.12706 v1 pith:TTZ6GUO2 submitted 2023-06-22 math.NA cs.NA

J. Haydel Collins , Alexei Lozinski , Guglielmo Scovazzi This is my paper · ORCID
classification math.NAcs.NA
keywords methodarbitraryboundaryconsistentorderpenalty-freeproveshifted
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We introduce and analyze a penalty-free formulation of the Shifted Boundary Method (SBM), inspired by the asymmetric version of the Nitsche method. We prove its stability and convergence for arbitrary order finite element interpolation spaces and we test its performance with a number of numerical experiments. Moreover, while the SBM was previously believed to be only asymptotically consistent (in the sense of Galerkin orthogonality), we prove here that it is indeed exactly consistent.

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