An adaptive high-order unfitted finite element method for elliptic interface problems
Numerical Analysis
2021-10-12 v3 Numerical Analysis
Abstract
We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse estimate which allows us to prove the stability of the finite element method under practical interface resolving mesh conditions and also prove the lower bound of the hp a posteriori error estimate. Numerical examples are included.
Cite
@article{arxiv.2009.01656,
title = {An adaptive high-order unfitted finite element method for elliptic interface problems},
author = {Zhiming Chen and Ke Li and Xueshuang Xiang},
journal= {arXiv preprint arXiv:2009.01656},
year = {2021}
}