Finite element solution of a class of parabolic integro-differential equations with inhomogeneous jump conditions using FreeFEM++

The finite element solution of a class of parabolic integro–partial differential equations with interfaces is presented. The spatial discretization is based on the triangular element while a two-step implicit scheme together with the trapezoidal method is employed for time discretization. For the spatial discretization, the elements in the neighborhood of the interface are more refined such that the interface is at \sigma$-distance from the approximate interface. The convergence rate of optimal order in L2-norm is analyzed with the assumption that the interface is arbitrary but smooth. Examples are given to support the theoretical findings with implementation on FreeFEM++.