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Journal Articles SIAM Journal on Scientific Computing Year : 2021

An unfitted Hybrid High-Order method with cell agglomeration for elliptic interface problems

Abstract

We design and analyze a Hybrid High-Order (HHO) method on unfitted meshes to approximate elliptic interface problems by means of a consistent penalty methodà la Nitsche. The curved interface can cut through the mesh cells in a rather general fashion. Robustness with respect to the cuts is achieved by using a cell-agglomeration technique, and robustness with respect to the contrast in the diffusion coefficients is achieved by using a different gradient reconstruction on each side of the interface. A key novel feature of the gradient reconstruction is to incorporate a jump term across the interface, thereby releasing the Nitsche penalty parameter from the constraint of being large enough. Error estimates with optimal convergence rates are established. A robust cell-agglomeration procedure limiting the agglomerations to the nearest neighbors is devised. Numerical simulations for various interface shapes corroborate the theoretical results.
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Dates and versions

hal-02280426 , version 1 (06-09-2019)
hal-02280426 , version 2 (05-06-2020)
hal-02280426 , version 3 (14-10-2020)
hal-02280426 , version 4 (11-12-2020)
hal-02280426 , version 5 (22-01-2021)

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Cite

Erik Burman, Matteo Cicuttin, Guillaume Delay, Alexandre Ern. An unfitted Hybrid High-Order method with cell agglomeration for elliptic interface problems. SIAM Journal on Scientific Computing, 2021, 43 (2), pp.A859-A882. ⟨10.1137/19M1285901⟩. ⟨hal-02280426v5⟩
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