In this work, a finite element scheme is proposed using a method of Euler-Taylor-Galerkin described in Páez (2016), for a non-linear model which describes the behavior of a new chemo-fluidic oscillator (Donea, 1984). This model is expressed by the coupling of an ordinary differential equation describing the hydrogel dynamics, the non-linear transport equation and an auxiliary equation determining the flux volume. The numerical solution is constructed by taking a semi-discretization in time of the transport equation, employing forward-time Taylor series expansions including time derivatives of second order and third order, avoiding instabilities problems. In this semi discrete equation, the spatial variable is approximated by the finite element formulation according to Galerkin. Some simulations are carried out taking different initial conditions for the concentration of the hydrogel. The numerical results describe the oscillatory behavior of the system as in Donea (1984), where MatLab tools are used as black box.