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 à 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.