A Taylor-Galerkin method for the use of finite elements in a nonlinear problem for the numerical modeling of a new Chemo-Fluid oscillator

In this work, a finite element scheme is proposed using a method of Euler-Taylor-Galerkindescribed inPaez (2016), for a non-linear model which describes the behavior of a new chemofluidicoscillator (Donea, 1984). This model is expressed by the coupling of an ordinarydifferential equation describing the hydrogel dynamics, the non-linear transport equation and anauxiliary equation determining the flux volume. The numerical solution is constructed by taking asemi-discretization in time of the transport equation, employing forward-time Taylor seriesexpansions including time derivatives of second order and third order, avoiding instabilitiesproblems. In this semi discrete equation, the spatial variable is approximated by the finite elementformulation according to Galerkin. Some simulations are carried out taking different initialconditions for the concentration of the hydrogel. The numerical results describe the oscillatorybehavior of the system as in Donea (1984), where MatLab tools are used as black box.