Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation

We continue the study of the nonconforming multiscale finite element method (Ms- FEM) introduced in 17, 14 for second order elliptic equations with highly oscillatory coefficients. The main difficulty in MsFEM, as well as other numerical upscaling methods, is the scale resonance effect. It has been show that the leading order resonance error can be effectively removed by using an over-sampling technique. Nonetheless, there is still a secondary cell resonance error of O(Є^2/h^2). Here, we introduce a Petrov-Galerkin MsFEM formulation with nonconforming multiscale trial functions and linear test functions. We show that the cell resonance error is eliminated in this formulation and hence the convergence rate is greatly improved. Moreover, we show that a similar formulation can be used to enhance the convergence of an immersed-interface finite element method for elliptic interface problems

Convergence of a nonconforming multiscale finite element method

The multiscale finite element method (MsFEM) [T. Y. Hou, X. H. Wu, and Z. Cai, Math. Comp., 1998, to appear; T. Y. Hou and X. H. Wu, J. Comput. Phys., 134 (1997), pp. 169-189] has been introduced to capture the large scale solutions of elliptic equations with highly oscillatory coefficients. This is accomplished by constructing the multiscale base functions from the local solutions of the elliptic operator. Our previous study reveals that the leading order error in this approach is caused by the "resonant sampling," which leads to large error when the mesh size is close to the small scale of the continuous problem. Similar difficulty also arises in numerical upscaling methods. An oversampling technique has been introduced to alleviate this difficulty [T. Y. Hou and X. H. Wu, J. Comput. Phys., 134 (1997), pp. 169-189]. A consequence of the oversampling method is that the resulting finite element method is no longer conforming. Here we give a detailed analysis of the nonconforming error. Our analysis also reveals a new cell resonance error which is caused by the mismatch between the mesh size and the wavelength of the small scale. We show that the cell resonance error is of lower order. Our numerical experiments demonstrate that the cell resonance error is generically small and is difficult to observe in practice

Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces

The well-known translation between the power law of the energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems

Description of a new species of Forcipomyia (Euprojoannisia) Brèthes, 1914 (Diptera: Ceratopogonidae) and a key to Chinese species of the subgenus

Forcipomyia (Euprojoannisia) coronacella Han et Hou sp. n. (Diptera: Ceratopogonidae) is described and illustrated based on male specimens from China. The new species is compared with the similar congeners, F. (Euprojoannisia) palustris (Meigen, 1804) and F. (Euprojoannisia) mucronis Liu et Yu, 2001. We provide separate keys for identification of the males and females of the species of the subgenus F. (Euprojoannisia) Brèthes in China

Withaferin A induces apoptosis in rat C6 glioma cells through regulating NF-ΚB nuclear translocation and activation of caspase cascade

Background: The demand for the chemopreventive drug from the plant source is increasing in recent times, owing to its various biological activities without any adverse effect. The intention of this current study was to examine the antiglioma effect of Withaferin A (WFA) on C6 glioma cell line model.Materials and Methods: C6 glioma cells were administrated with different concentration of WFA (50, 100, 200 and 500 μg/mL) and DMSO (control) group to examine its anti-proliferative, anti-inflammatory and pro-apoptotic activities.Results: Treatment with WFA showed a significant decline in the glioma cell count in a dose-dependent manner and thus proving its anti-proliferative effect. Similarly, inflammatory markers were also substantially lowered upon treatment with different concentration of WFA. However, DNA fragmentation and apoptotic markers like Caspase-3 and 9 were concomitantly enhanced after co-cultured with different concentration of WFA and thus exhibiting its cytotoxicity efficacy. Furthermore, the protein expression of Bcl2 and Bax were markedly downregulated and upregulated respectively; upon treatment with WFA on C6 glioma cells.Conclusion: The outcome of this study evidently demonstrates that C6 glioma cells co-cultured with increased concentration of WFA, showed an anti-proliferative, anti-inflammatory and pro-apoptotic effect in a dose-dependent fashion.Keywords: Withaferin A, C6 glioma cells, anti-proliferative, anti-inflammatory, caspase, apoptosi