A Cut Cell Hybrid High-Order Method for Elliptic Problems with Curved Boundaries
We design a Hybrid High-Order method for elliptic problems on curved domains. The method uses a cut cell technique for the representation of the curved boundary and imposes Dirichlet boundary conditions using Nitsche’s method. The physical boundary can cut through the cells in a very general fashion and the method leads to optimal error estimates in the H1-norm.
The first author was partly supported by EPSRC Grant EP/P01576X/1. This work was initiated when the authors were visiting the Institut Henri Poincaré during the Fall 2016 Thematic Trimester “Numerical Methods for Partial Differential Equations”. The support of IHP is gratefully acknowledged.
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