An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, Part II Piecewise-smooth interfaces
<|reference_start|>An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, Part II Piecewise-smooth interfaces: We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the reliable cell merging algorithm for smooth interfaces to automatically generate the induced mesh for piecewise smooth interfaces. An $hp$ a posteriori error estimate is derived for a new unfitted finite element method whose finite element functions are conforming in each subdomain. Numerical examples illustrate the competitive performance of the method.<|reference_end|>
@article{chen2024an,
    title={An arbitrarily high order unfitted finite element method for elliptic
  interface problems with automatic mesh generation, Part II. Piecewise-smooth
  interfaces},
    author={Zhiming Chen and Yong Liu},
    journal={arXiv preprint arXiv:2403.03418},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.03418},
    primaryClass={math.NA cs.NA}
}