界面问题的参数友好型部分罚浸入有限元方法

Parameter-friendly partially penalized immersed finite element method for interface problems

针对抛物型界面问题,提出参数友好型部分罚浸入有限元方法,并推导出半离散和全离散格式的最优误差估计.该方法采用与界面无关的非拟合网格,并且无须人为选择罚参数即可保证稳定性,数值试验验证了该方法的有效性.

This paper presents a parameter-friendly partially penalized immersed finite element method for solving parabolic interface problems, and the optimal error estimates for the semi-discrete and fully discrete schemes are derived.The method adopts non-fitting mesh independent of interface and ensures the stability without selecting penalty parameters manually. Numerical experiments verify the effectiveness of the proposed method.