Optimal Order Error Estimates of a Modified Nonconforming Rotated Q1 IFEM for Interface Problems

Abstract

This paper presents a new numerical method and analysis for solving second-order elliptic interface problems. The method uses a modified nonconforming rotated Q1 immersed finite element (IFE) space to discretize the state equation required in the variational discretization approach. Optimal order error estimates are derived in L2-norm and broken energy norm. Numerical examples are provided to confirm the theoretical results.