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1.
Finite element error estimates for 3D exterior incompressible flow with nonzero velocity at infinity
Paul Deuring 《Numerische Mathematik》2009,114(2):233-270
We consider a stationary incompressible Navier–Stokes flow in a 3D exterior domain, with nonzero velocity at infinity. In
order to approximate this flow, we use the stabilized P1–P1 finite element method proposed by Rebollo (Numer Math 79:283–319,
1998). Following an approach by Guirguis and Gunzburger (Model Math Anal Numer 21:445–464, 1987), we apply this method to
the Navier–Stokes system with Oseen term in a truncated exterior domain, under a pointwise boundary condition on the artificial
boundary. This leads to a discrete problem whose solution approximates the exterior flow, as is shown by error estimates. 相似文献
2.
In this article, a class of nonlinear evolution equations – reaction–diffusion equations with time delay – is studied. By
combining the domain decomposition technique and the finite difference method, the results for the existence, convergence
and the stability of the numerical solution are obtained in the case of subdomain overlap and when the time-space is completely
discretized.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
We develop a variational method for the solution of biharmonic problems for a rectangular domain where, at one pair of its
opposite sides, the unknown function and its normal derivative take zero values, and, at the other pair, certain inhomogeneous
conditions are valid. The cases of semiinfinite and finite domain are considered. The method is based on the minimization
of a quadratic functional determining the deviation of the solution from the given inhomogeneous conditions in the norm of
L
2. To solve this variational problem, we apply the expansion of the solution in the systems of complex biharmonic functions
(the so-called Papkovich homogeneous solutions), which satisfy identically the given homogeneous conditions at the pair of
opposite sides of the rectangle. This representation of the solution is somewhat different from that proposed earlier [V.
F. Chekurin, “A variational method for the solution of direct and inverse problems of the theory of elasticity for a semiinfinite
strip,” Izv. Ross. Akad. Nauk, Mekh. Tverdogo Tela, No. 2, 58–70 (1999)]. We consider several variants of inhomogeneous boundary conditions arising in the problems of the two-dimensional
theory of elasticity. Finally, we give an example of applying the proposed method for the determination of stress distributions
in a rectangular area one of whose sides is rigidly fastened and the opposite one is subjected to the action of normal forces.
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 88–98, January–March, 2008. 相似文献
4.
In the relativistic theory of gravity, we analyze the solution for a static spherically symmetrical body in detail. Comparing
this solution with the Schwarzschild solution in general relativity, we find that they are essentially different in the domain
near the Schwarzschild sphere. This difference eliminates the possibility of a collapse leading to the formation of “black
holes.”
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 1, pp. 4–24, October, 1999. 相似文献
5.
V. Keblikas 《Lithuanian Mathematical Journal》2007,47(2):147-163
We study the time-periodic Stokes problem in the domain with cylindrical outlets to infinity in weighted function spaces.
We prove that there exists a unique solution with prescribed fluxes over the sections of outlets to infinity and that, in
each outlet, this solution tends to the corresponding time-periodic Poiseuille flow.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 177–195, April–June, 2007. 相似文献
6.
Boumediene Abdellaoui Tarik Mohamed Touaoula 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(3):271-288
In this paper we consider age structured equation with diffusion under nonlocal boundary condition and nonnegative initial
data. We prove existence, uniqueness and the positivity of the solution to the above problem. Our main result is to get an
exponential decay of the solution for large times toward such a study state. To this end we prove a weighted Poincaré–Wirtinger’s
type inequality in unbounded domain. 相似文献
7.
Ya. I. Belopol'skaya 《Journal of Mathematical Sciences》1999,97(4):4206-4224
A priori estimates for a solution to a system of fully nonlinear parabolic equations are obtained in a bounded domain under
the condition that the solution vanishes on the boundary of the domain. The method of obtaining a priori estimates is based
on the possibility of reducing the problem under consideration to the Cauchy problem for a scalar equation on a manifold without
boundary in some linear space. Bibliography: 9 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 46–71. 相似文献
8.
In this paper, we apply the boundary integral method to the steady rotating Navier–Stokes equations in exterior domain. Introducing
some open ball which decomposes the exterior domain into a finite domain and a infinite domain, we obtain a coupled problem
by the steady rotating Navier–Stokes equations in finite domain and a boundary integral equation without using the artificial
boundary condition. For the coupled problem, we show the existence of solution in a convex set. 相似文献
9.
We investigate the first mixed problem for a quasilinear hyperbolic equation of the second order with power nonlinearity in
a domain unbounded with respect to the space variables. The case of arbitrarily many space variables is considered. We establish
conditions for the existence and uniqueness of a solution of this problem independent of the behavior of the solution as |x| → + ∞. The indicated classes of existence and uniqueness are the spaces of locally integrable functions, and, furthermore,
the dimension of the domain does not limit the order of nonlinearity.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1523–1531, November, 2007. 相似文献
10.
Zhaosheng Feng 《Journal of Global Optimization》2008,40(4):623-636
In order to study the uniformly translating solution of some non-linear evolution equations such as the complex Ginzburg–Landau
equation, this paper presents a qualitative analysis to a Duffing–van der Pol non-linear oscillator. Monotonic property of
the bounded exact solution is established based on the construction of a convex domain. Under certain parametric choices,
one first integral to the Duffing–van der Pol non-linear system is obtained by using the Lie symmetry analysis, which constitutes
one of the bases for further work of obtaining uniformly translating solutions of the complex Ginzburg–Landau equation.
Dedicated to Professor G. Strang on the occasion of his 70th birthday 相似文献
11.
V. A. Solonnikov 《Journal of Mathematical Sciences》1998,92(6):4364-4385
The main result is an asymptotic formula for a solution to the conjugation problem for the Navier-Stokes equations describing
the slow motion of two immiscible liquids such that one of them occupies a bounded domain Ω1 ⊂ ℝ3, whereas the other occupies the exterior domain Ω2=ℝ4∖Ω. Such a formula was obtained for a solution to the exterior problem with sticking conditions on the boundary in the works
of Fischer, Hsiao, and Wendland. The result obtained is applied to the proof of the solvability of a free-boundary problem
describing a uniform drop in an infinite liquid. Bibliography: 10 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 16. 1997, pp. 208–238. 相似文献
12.
We establish conditions for the existence and uniqueness of a solution of the mixed problem for the ultraparabolic equation
{fx1870-01} in an unbounded domain with respect to the variables x.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1661–1673, December, 2007. 相似文献
13.
R. B. Salimov 《Russian Mathematics (Iz VUZ)》2011,55(11):38-48
We propose a modification of the approach proposed by us in Russian Mathematics (Iz. VUZ) 44 (2), 58–62 (2000) for the solution of the Hilbert boundary-value problem for an analytic function in a multiconnected circular
domain. This approach implies the solution of the corresponding homogeneous problem including the determination of an analytic
function from the known boundary values of its argument in a circular domain. 相似文献
14.
V. P. Mikhailov 《Theoretical and Mathematical Physics》2008,157(3):1733-1744
We find a sufficient condition for the existence of a limit value of an elliptic equation solution on the domain boundary.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 436–449, December, 2008. 相似文献
15.
A. A. Arkhipova 《Journal of Mathematical Sciences》1996,80(6):2208-2225
The partial regularity up to the boundary of a domain is established for a solution u ∈ H1 (Ω) ∩ L∞ (Ω) to the boundary-value problem for a second-order elliptic system with strong nonlinearity in the case of dimension n≥3.
Bibliography: 12 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 15, 1995, pp. 47–69. 相似文献
16.
Interior error estimates are obtained for a low order finite element introduced by Arnold and Falk for the Reissner–Mindlin
plates. It is proved that the approximation error of the finite element solution in the interior domain is bounded above by
two parts: one measures the local approximability of the exact solution by the finite element space and the other the global
approximability of the finite element method. As an application, we show that for the soft simply supported plate, the Arnold–Falk
element still achieves an almost optimal convergence rate in the energy norm away from the boundary layer, even though optimal
order convergence cannot hold globally due to the boundary layer. Numerical results are given which support our conclusion.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
17.
Summary. A finite element formulation is developed for the two dimensional nonlinear time dependent compressible Navier–Stokes equations
on a bounded domain. The existence and uniqueness of the solution to the numerical formulation is proved. An error estimate
for the numerical solution is obtained.
Received September 9, 1997 / Revised version received August 12, 1999 / Published online July 12, 2000 相似文献
18.
We consider the Stokes problem in an axisymmetric three-dimensional domain with data which are axisymmetric and have angular component equal to zero. We observe that the solution is also axisymmetric and the velocity has also zero angular component, hence the solution satisfies a system of equations in the meridian domain. The weak three-dimensional problem reduces to a two-dimensional one with weighted integrals. The latter is discretized by Taylor–Hood type finite elements. A weighted Clément operator is defined and approximation results are proved. This operator is then used to derive the discrete inf–sup condition and optimal a priori error estimates. 相似文献
19.
Domain decomposition iterative procedures for solving scalar waves in the frequency domain 总被引:1,自引:0,他引:1
Seongjai Kim 《Numerische Mathematik》1998,79(2):231-259
The propagation of dispersive waves can be modeled relevantly in the frequency domain. A wave problem in the frequency domain
is difficult to solve numerically. In addition to having a complex–valued solution, the problem is neither Hermitian symmetric
nor coercive in a wide range of applications in Geophysics or Quantum–Mechanics. In this paper, we consider a parallel domain
decomposition iterative procedure for solving the problem by finite differences or conforming finite element methods. The
analysis includes the decomposition of the domain into either the individual elements or larger subdomains ( of finite elements). To accelerate the speed of convergence, we introduce relaxation parameters on the subdomain interfaces
and an artificial damping iteration. The convergence rate of the resulting algorithm turns out to be independent on the mesh
size and the wave number. Numerical results carried out on an nCUBE2 parallel computer are presented to show the effectiveness
of the method.
Received October 30, 1995 / Revised version received January 10, 1997 相似文献
20.
On the Unique Continuation Properties for Elliptic Operators with Singular Potentials 总被引:1,自引:0,他引:1
Xiang Xing TAO Song Yan ZHANG 《数学学报(英文版)》2007,23(2):297-308
Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato-Fefferman-Phong's class in Lipschitz domains. An elementary proof of the doubling property for u^2 over balls is presented, if the balls are contained in the domain or centered at some points near an open subset of the boundary on which the solution u vanishes continuously. Moreover, we prove the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations, and we derive the Bp weight properties for the solution u near the boundary. 相似文献