Anisotropic mesh adaption for time‐dependent problems

We propose a space–time adaptive procedure for a model parabolic problem based on a theoretically sound anisotropic a posteriori error analysis. A space–time finite element scheme (continuous in space but discontinuous in time) is employed to discretize this problem, thus allowing for non‐matching meshes at different time levels. Copyright © 2008 John Wiley & Sons, Ltd.     

A new point-locating algorithm under three-dimensional hybrid meshes

When particles are traced individually in a numerical simulation of particle-fluid flow, a point-locating scheme is necessary to relate the coordinates of a given point to the grid cell containing it. A new point-locating scheme combining the advantages of the existing ones is presented in this paper. The new method is first explained in detail. Then its performance under three-dimensional hybrid meshes is compared with the existing approaches in the literature. The results show that the proposed method is efficient, multifunctional and easy to implement in a structured/unstructured fluid flow solver.     

多尺度有限元法结合分层网格模拟二维奇异摄动的两端边界层问题

通过摄动系数建立分层网格,用多尺度有限元法捕捉对流扩散方程的两端边界层,研究二维奇异摄动模型。基于分层网格并利用多尺度基函数刻画了边界层的微观信息,用有限的计算资源、较短的计算时间,得到了不依赖于摄动系数、一致稳定的模拟结果。     

Finite-Difference Methods for a Class of Strongly Nonlinear Singular Perturbation Problems

The paper is concerned with strongly nonlinear singularly perturbed bound- ary value problems in one dimension.The problems are solved numerically by finite- difference schemes on special meshes which are dense in the boundary layers.The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed.For the central scheme,error estimates are derived in a discrete L~1 norm.They are of second order and decrease together with the perturbation parameterε.The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically.Numerical results showε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.     

Sobolev型方程各向异性网格下Wilson元的高精度分析

1引言 Sobolev方程在流体穿过裂缝岩石的渗透理论,土壤中湿气的转移问题,不同介质的热传导问题等许多物理问题中都有广泛的应用,因此已有许多文献研究此方程[2,6,8,9,11]但这些研究都是基于对剖分的正则性条件或拟一致假设[7],即满足hk/pK≤C或h/h≤C,vK∈Th,其中hk,PK分别是一般单元K的最大直径和最大内切圆直径,h=maxhk,h=minhk,C是一个与h无关的正常数.     

Ibuprofen-loaded PCL meshes manufactured using rapid tooling for ocular orbital repair

This study investigated the manufacture of resorbable polycaprolactone/ibuprofen (PCL/IBP) meshes by injection molding for application in ocular orbital repair. The pore dimension sizes used demonstrate that micro-porous meshes can be manufactured by injection molding using a prototype mold. The mechanical properties were observed to be dependent on the material composition and morphology. Lower stiffness, strength and elongation at failure were observed for the 8 mm pore sized samples. The PCL/Ibuprofen meshes initially showed a fast drug release but after 3 days the release was slow and controlled. The cytotoxicity test results of the PCL/Ibuprofen meshes indicated that the large initial quantity of Ibuprofen released was too high and resulted in cell toxicity. However, after this initial release, the PCL/Ibuprofen meshes showed a good interaction with the cells seeded on their surface. The presence of a low concentration of Ibuprofen does not negatively influence cell viability in culture.     

Virtual Elements for the Reissner‐Mindlin plate problem

In this work, we present a virtual element method for the approximation of the plate bending problem in the Reissner‐Mindlin formulation. The proposed method follows the MITC approach of the FEM context. We construct a family of VEM spaces with arbitrary degree of accuracy that satisfies the conditions of the MITC philosophy. We perform some numerical tests which allow us to assess the convergence and the robustness of the method.     

Polygonal finite elements for incompressible fluid flow

We discuss the use of polygonal finite elements for analysis of incompressible flow problems. It is well‐known that the stability of mixed finite element discretizations is governed by the so‐called inf‐sup condition, which, in this case, depends on the choice of the discrete velocity and pressure spaces. We present a low‐order choice of these spaces defined over convex polygonal partitions of the domain that satisfies the inf‐sup condition and, as such, does not admit spurious pressure modes or exhibit locking. Within each element, the pressure field is constant while the velocity is represented by the usual isoparametric transformation of a linearly‐complete basis. Thus, from a practical point of view, the implementation of the method is classical and does not require any special treatment. We present numerical results for both incompressible Stokes and stationary Navier–Stokes problems to verify the theoretical results regarding stability and convergence of the method. Copyright © 2013 John Wiley & Sons, Ltd.     

基于非结构四边形网格的WENO格式

基于非结构四边形网格发展求解双曲守恒律的三阶加权基本无振荡（WENO）格式.针对任意非结构四边形网格选取重构模板，并给出基于线性多项式的三阶线性重构.但对于一般的非结构四边形网格，会出现非常大的线性权和负权，使得非线性重构的WENO格式对光滑问题也不稳定.本文给出一个处理非常大的线性权的优化重构方法，对优化后得到的负线性权采用分裂方法进行处理.对于非线性权，提出一种考虑局部网格和物理量间断的新光滑度量因子.采用优化重构方法和新的非线性权，当前的三阶WENO格式在质量很差的网格上也具有很好的稳定性.理论的三阶精度在数值精度测试算例中得到验证，同时一范数和无穷范数的误差绝对值不依赖于网格质量；具有强间断的数值结果证明了当前格式的有效性.     

Creation of Chitosan-Based Nanocapsule-in-Nanofiber Structures for Hydrophobic/Hydrophilic Drug Co-Delivery and Their Dressing Applications in Diabetic Wounds

Nanofiber meshes (NFMs) loaded with therapeutic agents are very often employed to treat hard-to-heal wounds such as diabetic wounds. However, most of the NFMs have limited capability to load multiple or hydrophilicity distinctive-therapeutic agents. The therapy strategy is therefore significantly hampered. To tackle the innate drawback associated with the drug loading versatility, a chitosan-based nanocapsule-in-nanofiber (NC-in-NF) structural NFM system is developed for simultaneous loading of hydrophobic and hydrophilic drugs. Oleic acid-modified chitosan is first converted into NCs by the developed mini-emulsion interfacial cross-linking procedure, followed by loading a hydrophobic anti-inflammatory agent Curcumin (Cur) into the NCs. Sequentially, the Cur-loaded NCs are successfully introduced into reductant-responsive maleoyl functional chitosan/polyvinyl alcohol NFMs containing a hydrophilic antibiotic Tetracycline hydrochloride. Having a co-loading capability for hydrophilicity distinctive agents, biocompatibility, and a controlled release property, the resulting NFMs have demonstrated the efficacy on promoting wound healing either in normal or diabetic rats.