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To meet the demanding requirements in plug-in hybrid electric vehicles (PHEVs) or electric vehicles (EVs), higher energy density materials, such as the Li-rich, layered manganese-based oxides (LLOs) with the general formula xLi 2 MnO 3 ·(1-x)LiTMO 2 (TM = Mn, Ni, Co, etc.), are promising candidates as they possess higher reversible capacity (>250 mAh g −1 ), improved safety and much reduced cost. [4][5][6][7][8][9] Recent microscopic evidence reveals the intergrowth of rhombohedral LiTMO 2 (R-3m) and the monoclinic Li 2 MnO 3 -like layered structure (C/2m) at the atomic scale in the oxide grains. [10] The Li 2 MnO 3 component serves as an electrochemically active phase for Li storage when cycled above 4.5 V versus Li/Li + . [8,[11][12][13][14] Nevertheless, these LLO materials undergo steady voltage/capacity decay when cycled above 4.5 V, resulting in a substantial decrease of the cathode energy density. [15][16][17][18] The origin of voltage/capacity decay upon cycling stems from cation migration between TM layers and Li layers and subsequent phase transformation. [19,20] The cationic doping with other metallic cations (such as Mg, [21] Al, [22] Ti, [23] Sn, [24] Ru, [25] Y, [26] Zn, [27] etc.) and polyanion doping based on nonmetal elements, such as BO 4 5− , [28] SiO 4 4− , [29] PO 4 3-, [30] etc., have been employed to improve the cyclic durability by weakening the TM-O covalency in the oxygen closepacked structure. In addition, surface coatings using metal oxides, [31][32][33][34] fluorides and phosphates, [35][36][37] LiNiPO 4 and Li 3 VO 4 , [38][39][40] have been applied to protect the surface structure from side reactions with the electrolyte under high voltage and to restrain the layered-to-spinel transformation which occurs preferentially on the crystal surface and leads to capacity fading of LLO materials. However, the ionic dopants and coating materials are mostly electrochemically inactive, so the improved cycling stability is achieved at the expense of reduced specific capacity/energy density of the cathode. Moreover, a conformal and continuous coating on the surface of oxide particles is rather difficult to obtain practically. Hence, advancing the structural and cycling stability in both the bulk material and the surface structure through a simple way is highly desired for potential applications of LLO materials.Herein, we develop a novel LLO material with a nanoscaled spinel-like surface layer through gradient doping of polyanions Surface Structural Transition Induced by Gradient Polyanion-Doping in Li-Rich Layered Oxides: Implications for Enhanced Electrochemical PerformanceYing Zhao, Jiatu Liu, Shuangbao Wang, Ran Ji, Qingbing Xia, Zhengping Ding, Weifeng Wei,* Yong Liu, Peng Wang,* and Douglas G. Ivey Lithium-rich layered oxides (LLOs) exhibit great potential as high-capacity cathode materials for lithium-ion batteries, but usually suffer from capacity/ voltage fade during electrochemical cycling. Herein, a gradient polyaniondoping strategy is developed to initiate surface structural trans...

We explore the use of the non-symmetric Nitsche method for the weak imposition of boundary and coupling conditions along interfaces that intersect through a finite element mesh. In contrast to symmetric Nitsche methods, it does not require stabilization and therefore does not depend on the appropriate estimation of stabilization parameters. We first review the available mathematical background, recollecting relevant aspects of the method from a numerical analysis viewpoint. We then compare accuracy and convergence of symmetric and non-symmetric Nitsche methods for a Laplace problem, a Kirchhoff plate, and in 3D elasticity. Our numerical experiments confirm that the non-symmetric method leads to reduced accuracy in the L2" role="presentation"> error, but exhibits superior accuracy and robustness for derivative quantities such as diffusive flux, bending moments or stress. Based on our numerical evidence, the non-symmetric Nitsche method is a viable alternative for problems with diffusion-type operators, in particular when the accuracy of derivative quantities is of primary interest. KeywordsImmersed finite element methods, Weak boundary and coupling conditions, Non-symmetric Nitsche method AbstractWe explore the use of the non-symmetric Nitsche method for the weak imposition of boundary and coupling conditions along interfaces that intersect through a finite element mesh. In contrast to symmetric Nitsche methods, it does not require stabilization and therefore does not depend on the appropriate estimation of stabilization parameters. We first review the available mathematical background, recollecting relevant aspects of the method from a numerical analysis viewpoint. We then compare accuracy and convergence of symmetric and non-symmetric Nitsche methods for a Laplace problem, a Kirchhoff plate, and in 3D elasticity. Our numerical experiments confirm that the non-symmetric method leads to reduced accuracy in the L 2 error, but exhibits superior accuracy and robustness for derivative quantities such as diffusive flux, bending moments or stress. Based on our numerical evidence, the non-symmetric Nitsche method is a viable alternative for problems with diffusion-type operators, in particular when the accuracy of derivative quantities is of primary interest.

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