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991.
Erich Novak 《Numerische Mathematik》1986,50(2):245-252
Summary The definition of the average error of numerical methods (by example of a quadrature formula
to approximateS(f)= f d on a function classF) is difficult, because on many important setsF there is no natural probability measure in the sense of an equidistribution. We define the average a posteriori error of an approximation
by an averaging process over the set of possible information, which is used by
(in the example of a quadrature formula,N(F)={(f(a
1), ...,f/fF} is the set of posible information). This approach has the practical advantage that the averaging process is related only to finite dimensional sets and uses only the usual Lebesgue measure. As an application of the theory I consider the numerical integration of functions of the classF={f:[0,1]/f(x)–f(y)||x–y|}. For arbitrary (fixed) knotsa
i
we determine the optimal coefficientsc
i
for the approximation
and compute the resulting average error. The latter is minimal for the knots
. (It is well known that the maximal error is minimal for the knotsa
i
.) Then the adaptive methods for the same problem and methods for seeking the maximum of a Lipschitz function are considered. While adaptive methods are not better when considering the maximal error (this is valid for our examples as well as for many others) this is in general not the case with the average error. 相似文献
992.
Summary A scheme that uses singular perturbation theory to improve the performance of existing finite element methods is presented. The proposed scheme improves the error bounds of the standard Galerkin finite element scheme by a factor of O(n+1) (where is the small parameter andn is the order of the asymptotic approximation). Numerical results for linear second order O.D.E.'s are given and are compared with several other schemes. 相似文献
993.
Rüdiger Verfürth 《Numerische Mathematik》1986,50(6):697-721
Summary We consider a mixed finite element approximation of the stationary, incompressible Navier-Stokes equations with slip boundary condition, which plays an important rôle in the simulation of flows with free surfaces and incompressible viscous flows at high angles of attack and high Reynold's numbers. The central point is a saddle-point formulation of the boundary conditions which avoids the well-known Babuka paradox when approximating smooth domains by polyhedrons. We prove that for the new formulation one can use any stable mixed finite element for the Navier-Stokes equations with no-slip boundary condition provided suitable bubble functions on the boundary are added to the velocity space. We obtain optimal error estimates under minimal regularity assumptions for the solution of the continous problem. The techniques apply as well to the more general Navier boundary condition. 相似文献
994.
Robert Kosler 《Numerische Mathematik》1986,50(1):45-55
Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu
h in the norm of a suitable space
. Sufficient conditions for the uniform boundedness u
h
Z
=O(1) ash0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain
. The approximating subspaces are finite element spaces. Especially the caseX=W
0
m, p
(), 1<p<,Y=W
0
m. 2
(),Z=W
0
m. max (2,p)
()Wm, () is treated. Some examples for 1<p<2 are considered. Forp2 a refined technique is introduced in the author's paper [7]. 相似文献
995.
996.
Chen-Xi Zhang Zhi-Liang Liu Dai-Zheng Liao Zong-Hui Jiang Shi-Ping Yan 《Journal of Molecular Structure》2003,650(1-3):21-26
A novel complex [Cu(NIT2Py)(PDA)(H2O)]·(CH3OH)(H2O) has been synthesized and structurally characterized by X-ray diffraction methods. It crystallizes in the monoclinic space group P2(1)/c. The structure consists of [Cu(NIT2Py)(PDA)(H2O)] moiety, one solvent methanol molecule and one water molecule. The copper(II) ion is in a distorted octahedral environment: one nitrogen atom and one oxygen atom from the NIT2Py, one nitrogen atom from the PDA (2,6-pyridine dicarboxylic acid) and one oxygen atom from the aqueous in the basal plane; two oxygen atoms from the PDA in the axial position. The units of [Cu(NIT2Py)(PDA)(H2O)] were connected as one dimension chain by the intermolecular hydrogen bonds. The complex exhibits intramolecular antiferromagnetic interactions between the Cu(II) ion and the NIT2Py. 相似文献
997.
Wei-Chieh YangXin-An Lu Suvarn S KulkarniShang-Cheng Hung 《Tetrahedron letters》2003,44(42):7837-7840
A triethylsilane-reductive etherification of the trimethylsilyl ethers with a variety of carbonyl compounds in good yields at room temperature employing 0.5 mol% Cu(OTf)2 as an extremely efficient catalyst is described here. 相似文献
998.
荧光法研究Ge-132对牛血清白蛋白Maillard反应的抑制作用 总被引:2,自引:0,他引:2
人体内氨基酸及蛋白质的非酶糖化反应(Maillard反应)与糖尿病及其并发症的关系已经引起广泛注意[1].有机锗化合物β-羧乙基锗倍半氧化物(Ge-132)具有预防糖尿病及调节糖代谢的作用[2]. 相似文献
999.
不对称亚砜与1,10—双(1‘苯基—3’—甲基—5‘氧化吡唑—4’—基)癸二酮—[1,10]对… 总被引:1,自引:0,他引:1
1000.
TiO2(B) nanowires and TiO2 anatase nanowires were synthesized by the hydrothermal processing in 10 M NaOH aq. at 150 °C followed by the post-heat treatment at 300-800 °C. As-synthesized Na-free titanate nanowires (prepared by the hydrothermal treatment and repeated ion exchanging by HCl (aq.) were transformed into TiO2(B) structure with maintaining 1-D morphology at 300-500 °C, and further transformed into anatase structure at 600-800 °C with keeping 1-D shape. At 900 °C, they transformed into rod-shaped rutile grains. Microstructure of these 1-D TiO2 nanomaterials is reported. 相似文献