High order interface-penalty finite element methods for elliptic interface problems with Robin jump conditions

In this paper, we propose high-order interface penalty finite element methods for elliptic interface problems with Robin interface jump conditions. We employ the delicate weighting trick and the general Nitsche’s method to ensure the stability and robustness, respectively. Optimal error estimates are proven in the energy norm for the schemes. The error estimates are independent of both the cut configurations and the asymptotic parameter. A series of three-dimensional numerical results confirm the robustness and efficiency of the proposed methods. •High-order methods are proposed for elliptic interface problems with Robin jump conditions.•Optimal and robust error estimates are proven in energy norms for the proposed methods.•A series of three-dimensional numerical results support the analytical results.