Finite element methods for elliptic and parabolic interface problems

Abstract

The main objective of this thesis is to study the convergence of finite element solutions to the exact solutions of elliptic and parabolic interface problems by means of classical finite element method. Due to low global regularity of the true solution it is difficult to apply the classical finite element analysis to obtain optimal order of convergence for interface problems (cf. [3, 14]). The emphasis is on the theoretical aspects of such methods. In order to maintain the best possible convergence rate, a finite element discretization is proposed and analyzed for both elliptic and parabolic interface problems. More precisely, we have shown that the finite element solution converges to the exact solution at an optimal rate in L2 and H1 norms if the grid lines coincide with the actual interface by allowing interface triangles to be curved triangles. further, if the grid lines form an ...