We design and analyze a Hybrid High-Order (HHO) method on unfitted meshes to approximate elliptic interface problems by means of a consistent penalty method \'a 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.
An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems / Burman, E.; Cicuttin, M.; Delay, G.; Ern, A.. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - 43:2(2021), pp. 859-882. [10.1137/19M1285901]
An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems
Cicuttin M.;
2021
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 method \'a 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.File | Dimensione | Formato | |
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An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems _ SIAM Journal on Scientific Computing _ Vol. 43, No. 2 _ Society for Industrial and Applied Mathematics.pdf
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https://hdl.handle.net/11583/2978972