Stabilized Variational Formulation for Solving Cell Response to Applied Electric Field

In this work a stabilized variational formulation is proposed to solve the interface problem describing the electric response of cells to an applied electric field. The proposed stabilized formulation is attractive since the discrete operator resulting from finite element discretization generates a definite linear system for which efficient iterative solvers can be applied. The interface problem describing the cell response is solved with a primal variational formulation and the proposed stabilized formulation. Both methods are compared in terms of the approximation properties of the primal and the Lagrange multiplier variable. The computational performance of the methods are also compared in terms of the mean number of iterations needed to solve one time step during the polarization process of an isolated square cell. Moreover, numerical experiments are performed to validate the convergence properties of the methods.