Unconditional stability and error estimates of FEMs for the electro-osmotic flow in micro-channels
This provides a reliable numerical method for simulating electro-osmotic flows in micro-channels, which is incremental as it builds on existing finite element approaches.
The paper tackled the simulation of electro-osmotic flow in micro-channels by developing a finite element method with a backward Euler time-discrete scheme, achieving unconditional stability and optimal convergence rates as proven theoretically and validated numerically.
In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density $Ï^e$. A time-discrete method based on the backward Euler method is designed. The theoretical analysis shows that the numerical algorithm is unconditionally stable and has optimal convergence rates. To show the effectiveness of the proposed model, some numerical results for the electro-osmotic flow in the T-junction micro-channels and in rough micro-channels are provided. Numerical results indicate that the proposed numerical method is suitable for simulating electro-osmotic flows.