High-order primal mixed finite element method for boundary-value correction on curved domain
<|reference_start|>High-order primal mixed finite element method for boundary-value correction on curved domain: This paper addresses the non-homogeneous Neumann boundary condition on domains with curved boundaries. We consider the Raviart-Thomas element (RTk ) of degree $k \geq 1 $on triangular mesh. on a triangular mesh. A key feature of our boundary value correction method is the shift from the true boundary to a surrogate boundary. We present a high-order version of the method, achieving an $O(h^k+1/2)$ convergence in $L^2$-norm estimate for the velocity field and an $O(h^k )$ convergence in $H^1$-norm estimate for the pressure. Finally, numerical experiments validate our theoretical results.<|reference_end|>
@article{hou2024high-order,
    title={High-order primal mixed finite element method for boundary-value
  correction on curved domain},
    author={Yongli Hou, Yi Liu and Tengjin Zhao},
    journal={arXiv preprint arXiv:2410.00687},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.00687},
    primaryClass={math.NA cs.NA}
}