A locally modified second-order finite element method for interface problems and its implementation in 2 dimensions

The locally modified finite element method, which is introduced in Frei and Richter [ SIAM J. Numer. Anal. 52 (2014) 2315–2334], a simple fitted method that able to resolve weak discontinuities interface problems. based on fixed structured coarse mesh, then refined into sub-elements an interior interface. In this work, we extend the two space dimensions second order using isoparametric approach elements. Thereby need take care resulting curved edges do not lead degenerate sub-elements. We prove optimal priori error estimates L 2 -norm discrete energy norm. Finally, present numerical examples substantiate theoretical findings.