(A) structured grid method for robin type jump along interface

Abstract

The finite element method is developed to solve the partial differential equations (PDEs) numerically. Moreover, the immersed finite element method is invented for PDEs with general interface. In this thesis, we develop a numerical scheme for solving an elliptic PDE with Robin type jump along interface. First, we introduce a biological model problem. Focusing on a simple case, we recall the usual P1 conforming-based finite elements and modify them to satisfy our problem locally. Next, we define a bilinear form to make a weak equation. Finally, we solve the problem numerically with several interface cases and show that the expected convergence order is obtained. Furthermore, we bring this paper to an end with an appendix of the details for a numerical line integration in our bilinear form.