The optimal convergence analysis for an immersed finite element method

Abstract

We present a new proof for optimal-convergence of an immersed interface finite element method based on linear polynomials on non-interface triangular elements and modified linear polynomials on interface triangular elements. Optimal-order error estimates are derived in the broken H1-norm and L2-norm by using the well-known bilinear lemma. The proof seems to be more concise and direct.