共查询到19条相似文献,搜索用时 62 毫秒
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证明了各向异性泛函的极小点与各向异性方程 相似文献
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设A是Rn上的各向异性伸缩, L是由各向异性Calderón-Zygmund算子生成的一般的多线性算子.本文得到L从加权Lebesgue空间Lwp(Rn)到无权的各向异性Hardy空间HAp (Rn)的有界性.另外,对各向异性Hardy空间H1(Rn)和加权各向异性BMO空间BMOAw(Rn)得到包含关系:BMOAw(Rn)■(H1A(Rn))*.作为应用,对加权各向异性BMO函数b和各向异性Calderón-Zygmund算子T生成的交换子[T, b],得到‖[T, b](f)‖Lwp(Rn)C‖b‖BMOwA(Rn)‖f‖Lpw(Rn).以上所有结果在经典的各向齐性情形下也是新的. 相似文献
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本文探讨了磁场、流场、各向异性热流和各向异性外热源以及库仑碰撞和内波粒相互作用对压强各向异性演化的影响.并根据定常太阳风这样的磁化等离子体中不存在与粘性应力无关的各向异性静压强的分析结论,证明了可用平行和垂直磁场压强场以及流场,来计算太阳风的粘性效应,而太阳风粘性模式实际上是包含质子热各向异性的太阳风模式.这种模式适于描写各类太阳风的粘性效应,包括能用经典理论描写的冕旒低速流;对于冕洞高速流,在能量方程中应包含各向异性质子热传导和各向异性外热源(如Alfven涨落加热). 相似文献
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在物理表象的规范空间下研究了静电磁场方程,推导出了一阶模态形式的各向异性介质静电磁场的基本求解方程,从而得到了如下的理论结论:各向同性介质电或磁场为标量场;各向异性介质电或磁场则为失量场,其大小和方向与介质的异性子空间有关.以电各向异性介质为例,具体讨论了各向异性电场的规律. 相似文献
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Anisotropic meshes are known to be well-suited for problems which exhibit anisotropic solution features.Defning an appropriate metric tensor and designing an efcient algorithm for anisotropic mesh generation are two important aspects of the anisotropic mesh methodology.In this paper,we are concerned with the natural metric tensor for use in anisotropic mesh generation for anisotropic elliptic problems.We provide an algorithm to generate anisotropic meshes under the given metric tensor.We show that the inverse of the anisotropic difusion matrix of the anisotropic elliptic problem is a natural metric tensor for the anisotropic mesh generation in three aspects:better discrete algebraic systems,more accurate fnite element solution and superconvergence on the mesh nodes.Various numerical examples demonstrating the efectiveness are presented. 相似文献
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Gerd Kunert 《Numerical Methods for Partial Differential Equations》2002,18(5):625-648
Directional, anisotropic features like layers in the solution of partial differential equations can be resolved favorably by using anisotropic finite element meshes. An adaptive algorithm for such meshes includes the ingredients Error estimation and Information extraction/Mesh refinement. Related articles on a posteriori error estimation on anisotropic meshes revealed that reliable error estimation requires an anisotropic mesh that is aligned with the anisotropic solution. To obtain anisotropic meshes the so‐called Hessian strategy is used, which provides information such as the stretching direction and stretching ratio of the anisotropic elements. This article combines the analysis of anisotropic information extraction/mesh refinement and error estimation (for several estimators). It shows that the Hessian strategy leads to well‐aligned anisotropic meshes and, consequently, reliable error estimation. The underlying heuristic assumptions are given in a stringent yet general form. Numerical examples strengthen the exposition. Hence the analysis provides further insight into a particular aspect of anisotropic error estimation. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 625–648, 2002; DOI 10.1002/num.10023 相似文献
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We present a numerical scheme for modeling the electric field in the media with tensor conductivity. This scheme is based on vector finite element method in frequency domain. The numerical computations of the electric field in the anisotropic medium are done. The conductivity of the anisotropic medium is positive defined dense tensor in general case. We consider the electric field from anisotropic layer, inclined anisotropic layer and some anisotropic objects in isotropic half-space. 相似文献
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MAO Shipeng & SHI Zhongci Institute of Computational Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences PO Box Beijing China 《中国科学A辑(英文版)》2006,49(10)
In this paper, we consider the nonconforming rotated Q1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis. 相似文献
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In this paper, we consider the nonconforming rotated Q
1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral
meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing
another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic
affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements
whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which
coincides with our theoretical analysis. 相似文献
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Let $A$ be a general expansive matrix on $\mathbb{R}^n$. The aims of this article are twofold. The first one is to give a survey on the recent developments of anisotropic Hardy-type function spaces on $\mathbb{R}^n$, including anisotropic Hardy–Lorentz spaces, anisotropic variable Hardy spaces and anisotropic variable Hardy–Lorentz spaces as well as anisotropic Musielak–Orlicz Hardy spaces. The second one is to correct some errors and seal some gaps existing in the known articles. Some unsolved problems are also presented. 相似文献
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In this paper, we consider the nonconforming rotated Q 1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis. 相似文献
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In this paper,we prove a sharp anisotropic L;Minkowski inequality involving the total Lpanisotropic mean curvature and the anisotropic p-capacity for any bounded domains with smooth boundary in Rn.As consequences,we obtain an anisotropic Willmore inequality,a sharp anisotropic Minkowski inequality for outward F-minimising sets and a sharp volumetric anisotropic Minkowski inequality.For the proof,we utilize a nonlinear potential theoretic approach which has been recently developed by Agostiniani et al.(2019). 相似文献
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The spectral densities for an anisotropic fractal surfaces are investigated. Since there is no general definition for anisotropic fractal surface, the profiles of anisotropic fractal surfaces are assumed to be fractal in two main axes. Then, the possible forms of the surface spectral densities are proposed. By using the inverse Fast Fourier Transform, anisotropic fractal surfaces can be simulated from the spectral densities. 相似文献