UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

Challenges of polymer electrolyte with wide electrochemical window for high energy solid-state lithium batteries

With the rapid development of energy storage technology,solid-state lithium batteries with high energy density,power density,and safety are considered as the ideal choice for the next generation of energy storage devices.Solid electrolytes have attracted considerable attention as key components of solid-state batteries.Compared with inorganic solid electrolytes,solid polymer electrolytes have better flexibility,machinability,and more importantly,better contact with the electrode,and low interfacial impedance.However,its low ionic conductivity,narrow electrochemical stability window(ESW),and poor mechanical properties at room temperature limit its development and practical applications.In recent years,many studies have focused on improving the ionic conductivity of polymer electrolytes;however,few systematic studies and reviews have been conducted on their ESWs.A polymer electrolyte with wide electrochemical window will aid battery operation at a high voltage,which can effectively improve their energy density.Moreover,their stability toward lithium metal anode is also important.Therefore,this review summarizes the recent progress of solid polymer electrolytes on the ESW,discusses the factors affecting ESW of polymer electrolytes,and analyzes a strategy to broaden the window from the perspective of molecular interaction,polymer structural design,and interfacial tuning.The development trends of polymer electrolytes with wide electrochemical windows are also presented.