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31.
Superconvergence of a Nonconforming Finite Element Approximation to Viscoelasticity Type Equations on Anisotropic Meshes 总被引:3,自引:0,他引:3
Dongyang Shi Yucheng Peng Shaochun Chen 《高等学校计算数学学报(英文版)》2006,15(4):375-384
The main aim of this paper is to study the approximation to viscoelasticity type equations with a Crouzeix-Raviart type nonconforming finite element on the anisotropic meshes. The superclose property of the exact solution and the optimal error estimate of its derivative with respect to time are derived by using some novel techniques. Moreover, employing a postprocessing technique, the global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is studied. 相似文献
32.
A non-equilibrium reacting flow methodology has been added to a conservative, monotonic, compressible flow solver to allow
numerical simulations of gas detonations. This flow solver incorporates unstructured dynamically adaptive meshes with the
Finite Element Method – Flux Corrected Transport (FEM-FCT) scheme, which has shown excellent predictive capability of various
non-reacting compressible flows. A two-step induction parameter model was used to model the combustion of the gas phase coupled
with an energy release equation which was simulated with a point implicit finite element scheme. This combustion model was
then applied to a two-dimensional detonation test case of a hypothetical fuel:oxygen mixture. The detonation simulation yielded two transverse waves which continued to propagate. This feature and
the detonation shock speed mean and fluctuations were found to be grid-independent based on a resolution of about twenty elements
within the average induction length. The resolution was efficiently achieved with the unstructured dynamically adaptive finite
elements, which were three orders of magnitude less in number then required for uniform discretization.
Received 26 August 1996 / Accepted 31 March 1997 相似文献
33.
基于非结构化同位网格的SIMPLE算法 总被引:4,自引:1,他引:4
通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散;扩散项的离散采用二阶中心差分格式;对于压力-速度耦合利用SIMPLE算法进行处理;计算节点的布置采用同位网格技术,界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算,讨论了非结构化同位网格有限体积法在实现SIMPLE算法时,迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知,本文的方法是准确和可信的。 相似文献
34.
35.
Martins A Alves da Silva ML Faria S Marques AP Reis RL Neves NM 《Macromolecular bioscience》2011,11(7):978-987
A specially designed electroconductive collector enables the electrospinning of P-NFM composed of areas of parallel/uniaxially aligned fibers and areas of random/orthogonal nanofiber distribution. The biological relevance of P-NFM is demonstrated using hBMSCs as an autologous cell source. The structures induce cell orientation along the uniaxially aligned fibers, mainly during earlier culturing periods under basal and osteogenic differentiation conditions. The microtopography of the P-NFM also controls the deposition of mineralized extracellular matrix along the pre-defined fiber direction. Genotypic characterization confirms the successful differentiation into the osteogenic lineage. 相似文献
36.
We present a new algorithm for generating layer-adapted meshes for the
finite element solution of singularly perturbed problems based on mesh partial differential equations (MPDEs). The ultimate goal is to design meshes that are similar
to the well-known Bakhvalov meshes, but can be used in more general settings:
specifically two-dimensional problems for which the optimal mesh is not tensor-product in nature. Our focus is on the efficient implementation of these algorithms,
and numerical verification of their properties in a variety of settings. The MPDE is
a nonlinear problem, and the efficiency with which it can be solved depends adversely on the magnitude of the perturbation parameter and the number of mesh
intervals. We resolve this by proposing a scheme based on $h$-refinement. We present
fully working FEniCS codes [Alnaes et al., Arch. Numer. Softw., 3 (100) (2015)]
that implement these methods, facilitating their extension to other problems and
settings. 相似文献
37.
主要目的是在各向异性网格下研究二阶椭圆特征值问题的两类非协调有限元—类Wilson矩形元和Carey三角形元—的收敛性分析.通过新的技巧和方法,得到了与传统有限元网格剖分下相同的特征对的最优误差估计.推广了已有的结果. 相似文献
38.
Adjoint‐based and feature‐based grid adaptive strategies are compared for their robustness and effectiveness in improving the accuracy of functional outputs such as lift and drag coefficients. The output‐based adjoint approach strives to improve the adjoint error estimates that relate the local residual errors to the global error in an output function via adjoint variables as weight functions. A conservative adaptive indicator that takes into account the residual errors in both the primal (flow) and dual (adjoint) solutions is implemented for the adjoint approach. The physics‐based feature approach strives to identify and resolve significant features of the flow to improve functional accuracy. Adaptive indicators that represent expansions and compressions in the flow direction and gradients normal to the flow direction are implemented for the feature approach. The adaptive approaches are compared for functional outputs of three‐dimensional arbitrary Mach number flow simulations on mixed‐element unstructured meshes. Grid adaptation is performed with h‐refinement and results are presented for inviscid, laminar and turbulent flows. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
39.
LIUGUOQING 《高校应用数学学报(英文版)》1995,10(4):427-438
A nonlinear difference scheme is given for solving a quasilinear siagularly perturbed two-point boundary value problem with a turning point. The method uses non-equidistant discretization meshes. The solution of the scheme is shown to be first order accurate in the discrete L^∞ norm, uniformly in the perturbation parameter. 相似文献
40.
Xiaohai Liao Ricardo H. Nochetto 《Numerical Methods for Partial Differential Equations》2003,19(4):421-442
Local a posteriori error estimators are derived for linear elliptic problems over general polygonal domains in 2d. The estimators lead to a sharp upper bound for the energy error in a local region of interest. This upper bound consists of H1‐type local error indicators in a slightly larger subdomain, plus weighted L2‐type local error indicators outside this subdomain, which account for the pollution effects. This constitutes the basis of a local adaptive refinement procedure. Numerical experiments show a superior performance than the standard global procedure as well as the generation of locally quasi‐optimal meshes. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 421–442, 2003 相似文献