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81.
Rüdiger Verfürth 《Numerische Mathematik》1986,50(6):685-695
Summary We consider a mixed finite element approximation of the three dimensional vector potential, which plays an important rôle in the simulation of perfect fluids and in the calculation of rotational corrections to transonic potential flows. The central point of our approach is a saddlepoint formulation of the essential boundary conditions. In particular, this avoids the wellknown Babuka paradox when approximating smooth domains by polyhedrons. Using piecewise linear/piecewise constant elements for the vector potential/the boundary terms, we obtain optimal error estimates under minimal regularity assumptions for the solution of the continuous problem. 相似文献
82.
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
83.
Summary Under suitable conditions, we prove the convergence of the Bateman method for integral equations defined over bounded domains inR
d
,d1. The proof makes use of Hilbert space methods, and requires the integral operator to be non-negative definite. For one-dimensional integral equations over finite intervals, estimated rates of convergence are obtained which depend on the smoothness of the kernel, but are independent of the inhomogeneous term. In particular, for aC
kernel andn reasonably spaced Bateman points, the convergence is shown to be faster than any power of 1/n. Numerical calculations support this result. 相似文献
84.
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
85.
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
86.
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
87.
This
study discussed the phenomena on thermal polymerization of α-methylstyrene
(AMS). A curve scanned by temperature-programmed technique was performed by
differential scanning calorimetry (DSC). Heat of polymerization (ΔH) and onset temperature of exothermic (T0) behavior were determined
to be 280±10 J g-1 and about 138±1°C,
respectively. A dimer formation mechanism was proposed for initiation of the
propagating chain. Spectroscopic identification of dimer structure was conducted
by infrared (IR) spectroscopy in the wavenumber from 650 to 1100 cm-1associated
with molecular fingerprint characteristics. The mechanism of thermal polymerization
on α-methylstyrene proposed in this study was similar to that of styrene
suggested by Mayo. 相似文献
88.
Klaus Hoechsmann 《Rendiconti del Circolo Matematico di Palermo》1995,44(1):5-20
Let ζ be a primitivesp-th root of unity for a primep>2, and consider the group Ω(ζ) of cyclotomic units in the ringR(ζ)=ℒ[ζ+ζ-1]. This paper deals with the image of Ω(ζ) in the unit group ofR(ζ)/qR(ζ), whereq is a prime ≠p. In particular, it obtains criteria for this image to be essentially everything, and a lower bound on the density of primesp (withq fixed) for which it cannot be. These results have a direct bearing on previous work about units in integral group rings for
cyclic groups of orderpq.
Work supported in part by an operating grant from NSERC (Canada). 相似文献
89.
Henrik Stetkaer 《Aequationes Mathematicae》1995,49(1):252-275
We study properties of solutionsf, g, h C(G) of the functional equation
相似文献
90.
A method to prove lower estimates for linear operators is introduced. As a result the best lower estimate for certain convolution operators, for the multivariate Bernstein-Durrmeyer operators in part I and the Bernstein polynomial operators in part II (see [10]), are obtained.Communicated by Hubert Berens 相似文献
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