The Convergence of the Bilinear and Linear Immersed Finite Element Solutions to Interface Problems

This article analyzes the error in both the bilinear and linear immersed finite element (IFE) solutions for second-order elliptic boundary problems with discontinuous coefficients. The discontinuity in the coefficients is supposed to happen across general curves, but the mesh of the IFE methods can be allowed not to align with the curve of discontinuity. It has been shown that the bilinear and linear IFE solutions converge to the exact solution under the usual assumptions about the meshes and regularity. (C) 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 312-330, 2012