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101.
Marc Küther 《Numerische Mathematik》2003,93(4):697-727
Summary. We introduce a new technique for proving a priori error estimates between the entropy weak solution of a scalar conservation
law and a finite–difference approximation calculated with the scheme of Engquist-Osher, Lax-Friedrichs, or Godunov. This technique
is a discrete counterpart of the duality technique introduced by Tadmor [SIAM J. Numer. Anal. 1991]. The error is related
to the consistency error of cell averages of the entropy weak solution. This consistency error can be estimated by exploiting
a regularity structure of the entropy weak solution. One ends up with optimal error estimates.
Received December 21, 2001 / Revised version received February 18, 2002 / Published online June 17, 2002 相似文献
102.
Using the classification of the finite simple groups, we classify all finite generalized polygons having an automorphism group acting distance-transitively on the set of points. This proves an old conjecture of J. Tits saying that every group with an irreducible rank 2 BN-pair arises from a group of Lie type.Research Associate of the National Fund for Scientific Research (Belgium). 相似文献
103.
We consider numerical methods for the incompressible Reynolds averaged Navier–Stokes equations discretized by finite difference
techniques on non-staggered grids in body-fitted coordinates. A segregated approach is used to solve the pressure–velocity
coupling problem. Several iterative pressure linear solvers including Krylov subspace and multigrid methods and their combination
have been developed to compare the efficiency of each method and to design a robust solver. Three-dimensional numerical experiments
carried out on scalar and vector machines and performed on different fluid flow problems show that a combination of multigrid
and Krylov subspace methods is a robust and efficient pressure solver.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
104.
Harry Yserentant 《Numerische Mathematik》1997,76(1):111-142
Summary. Fluid mechanics describes the motion of mass in space under the influence of internal and external forces. The particle model
presented in this article is based on this fact. The fluid is subdivided into a finite number of small mass packets, the particles.
These mass packets have a finite extension and share all properties with the fluid, except for the restriction that they cannot
get deformed and can perform only rigid body motions. The forces acting upon the particles are identical to those acting on
a part of a fluid. The exact conservation of mass and, for the case of adiabatic flows, also of entropy is automatically guaranteed
by the approach. When the particle size tends to zero, the mean local displacement of the particles converges in the weak
sense. In the inviscid case, the resulting flows can be regarded as solutions of the Euler equations.
Received February 17, 1995 / Revised version received December 28, 1995 相似文献
105.
Masao Ishikawa 《Journal of Combinatorial Theory, Series A》2006,113(1):113-155
The initial purpose of the present paper is to provide a combinatorial proof of the minor summation formula of Pfaffians in [Ishikawa, Wakayama, Minor summation formula of Pfaffians, Linear and Multilinear Algebra 39 (1995) 285-305] based on the lattice path method. The second aim is to study applications of the minor summation formula for obtaining several identities. Especially, a simple proof of Kawanaka's formula concerning a q-series identity involving the Schur functions [Kawanaka, A q-series identity involving Schur functions and related topics, Osaka J. Math. 36 (1999) 157-176] and of the identity in [Kawanaka, A q-Cauchy identity involving Schur functions and imprimitive complex reflection groups, Osaka J. Math. 38 (2001) 775-810] which is regarded as a determinant version of the previous one are given. 相似文献
106.
V. S. Titov 《Acta Appl Math》1989,15(1-2):137-147
The local symmetries and conservation laws are calculated for the equations of shallow water with an axisymmetric profile of bottom under the assumption that the corresponding generating functions may depend only on all variables and their derivatives up to the second order. It is shown that if the bottom has the form of a paraboloid of revolution, then there are many symmetries and conservation laws generalizing those for the case of plane bottom. 相似文献
107.
In this paper, the existence and the uniqueness of the global solution for the Cauchy problem of the generalized double dispersion equation are proved. The blow-up of the solution for the Cauchy problem of the generalized double dispersion equation is discussed by the concavity method under some conditions. 相似文献
108.
This work is concerned with the study of steady flows of an incompressible viscoelastic fluid of Oldroyd type, with viscosity depending on the second invariant of the rate of deformation tensor in an exterior domain. We establish a result of existence and uniqueness of strong solutions for sufficiently small data and give estimates relating these solutions to those of the corresponding generalized Newtonian fluid. 相似文献
109.
The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated.
The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model
still involves a kinetic variable, the particle energy in the rest frame of the fluid, but shares similarities with the compressible
Navier-Stokes equation of gas dynamics. Then a diffusive scaling is examined under the hypothesis of small perturbations of
a global equilibrium. In this case, the macroscopic model couples the usual incompressible Navier-Stokes with a diffusion
equation for the energy distribution function of the particles, constrained by an extended version of the Boussinesq relation.
In both cases, the effect of a Lorentz force term is developed, in the perspective of plasma physical modelling.
Received June 16, 1997 相似文献
110.
Darya Apushkinskaya Michael Bildhauer Martin Fuchs 《Journal of Mathematical Fluid Mechanics》2005,7(2):261-297
We consider the stationary flow of a generalized Newtonian fluid which is modelled by an anisotropic dissipative potential f. More precisely, we are looking for a solution
of the following system of nonlinear partial differential equations
Here
denotes the pressure, g is a system of volume forces, and the tensor T is the gradient of the potential f. Our main hypothesis imposed on f is the existence of exponents 1 < p q0 < such that
holds with constants , > 0. Under natural assumptions on p and q0 we prove the existence of a weak solution u to the problem (*), moreover we prove interior C1,-regularity of u in the two-dimensional case. If n = 3, then interior partial regularity is established. 相似文献
((*)) |