共查询到20条相似文献,搜索用时 15 毫秒
1.
研究了三维空间中带非线性阻尼项的可压缩欧拉方程组的初值问题.利用能量估计和傅立叶分析的方法,在初值是常状态附近的一个H~3∩L~1中的小扰动时获得了初值问题的解整体存在,并得到了解在大时间的L~2,L~∞衰减率分别为t~(-3/4),t~(-3/2),将线性阻尼的情形推广到了非线性阻尼的情形. 相似文献
2.
考虑在一般的三维无界区域中的具有滑移边界条件的带有阻尼的可压缩欧拉方程.当初始值接近平衡态时,获得了全局存在性和唯一性.同时,研究了在半空间情形下系统的衰减率.证明了经典解的L~2范数以(1+t)~(-3/4)衰减到常值背景解. 相似文献
3.
The authors investigate the global existence and asymptotic behavior
of classical solutions to the 3D non-isentropic compressible Euler
equations with damping on a bounded domain with slip boundary
condition. The global existence and uniqueness of classical
solutions are obtained when the initial data are near an
equilibrium. Furthermore, the exponential convergence rates of the
pressure and velocity are also proved by delicate energy methods. 相似文献
4.
Christian Rohde 《Numerische Mathematik》1998,81(1):85-123
Summary. Systems of nonlinear hyperbolic conservation laws in two space dimensions are considered which are characterized by the fact
that the coupling of the equations is only due to source terms. To solve these weakly coupled systems numerically a class
of explicit and implicit upwind finite volume methods on unstructured grids is presented. Provided an unique entropy solution
of the system of conservation laws exists we prove that the approximations obtained by these schemes converge for vanishing
discretization parameter to this entropy solution. These results are applied to examples from combustion theory and hydrology
where the existence of entropy solutions can be shown. The proofs rely on an extension of a result due to DiPerna concerning
measure valued solutions to the case of weakly coupled hyperbolic systems.
Received April 29, 1997 相似文献
5.
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
6.
Summary. In this paper we derive an error bound for the large time step, i.e. large Courant number, version of the Glimm scheme when used for the approximation
of solutions to a genuinely nonlinear, i.e. convex, scalar conservation law for a generic class of piecewise constant data.
We show that the error is bounded by for Courant numbers up to 1. The order of the error is the same as that given by Hoff and Smoller [5] in 1985 for the Glimm
scheme under the restriction of Courant numbers up to 1/2.
Received April 10, 2000 / Revised version received January 16, 2001 / Published online September 19, 2001 相似文献
7.
A fully discrete finite element method is used to approximate the electric field equation derived from time-dependent Maxwell's equations in three dimensional polyhedral domains. Optimal energy-norm error estimates are achieved for general Lipschitz polyhedral domains. Optimal -norm error estimates are obtained for convex polyhedral domains. Received February 3, 1997 / Revised version received February 27, 1998 相似文献
8.
研究了三维空间中带非线性阻尼项的可压缩等熵欧拉方程组Dirichlet初边值问题.采用泛函方法,定义几种不同的泛函,当初始速度足够大时分别得到了经典解在某一时间内必定爆破的结论.由于出现了非线性阻尼项,较之线性阻尼的情形,经典解爆破的难度随之增加. 相似文献
9.
Summary.
We prove convergence of a class of higher order upwind
finite
volume schemes on unstructured grids for scalar conservation laws in
several space dimensions. The result is applied to the discontinuous
Galerkin method due to Cockburn, Hou and Shu.
Received
April 15, 1993 / Revised version received March 13, 1995 相似文献
10.
In this paper, the existence and asymptotic behavior of C1 solutions to the multi-dimensional compressible Euler equations with damping on the framework of Besov space are considered. Comparing with the well-posedness results of Sideris–Thomases–Wang [T. Sideris, B. Thomases, D.H. Wang, Long time behavior of solutions to the three-dimensional compressible Euler with damping, Comm. Partial Differential Equations 28 (2003) 953–978], we weaken the regularity assumptions on the initial data. The global existence lies on a crucial a-priori estimate which is obtained by the spectral localization method. The main analytic tools are the Littlewood–Paley decomposition and Bony’s paraproduct formula. 相似文献
11.
12.
The Riemann problem for two-dimensional isentropic Euler equations is considered. The initial data are three constants in three fan domains forming different angles. Under the assumption that only a rarefaction wave, shock wave or contact discontinuity connects two neighboring constant initial states, it is proved that the cases involving three shock or rarefaction waves are impossible. For the cases involving one rarefaction (shock) wave and two shock (rarefaction) waves, only the combinations when the three elementary waves have the same sign are possible (impossible). 相似文献
13.
Haibo Cui Haiyan Yin Jinshun Zhang Changjiang Zhu 《Journal of Differential Equations》2018,264(7):4564-4602
In this paper, we are concerned with the asymptotic behavior of solutions to the system of Euler equations with time-depending damping, in particular, include the constant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Compared with previous results about Euler equations with constant coefficient damping obtained by Hsiao and Liu (1992) [2], and Nishihara (1996) [9], we obtain a general result when the initial perturbation belongs to the same space, i.e. . Our proof is based on the classical energy method. 相似文献
14.
Gabriele Engl 《Numerische Mathematik》1996,72(3):349-366
Summary.
A network formulation is introduced for the modeling and numerical simulation
of complex gas transmission systems like a multi-cylinder internal
combustion engine. Several simulation levels are discussed
which result in different network representations of a specific system.
Basic elements of a network are chambers of finite volume, straight pipes and
connections like valves or nozzles. The pipe flow is modeled by the unsteady,
one-dimensional Euler equations of gas dynamics. Semi-empirical approaches
for the chambers and the connections yield differential-algebraic equations
(DAEs) in time. The numerical solution is based on a TVD scheme for the pipe
equations and a predictor-corrector method for the DAE-system. Simulation results
for an internal combustion engine demonstrate the practical
interest of the new approach.
Received
May 12, 1994 / Revised version received August 26, 1994 相似文献
15.
Alexander N. Malyshev 《Numerische Mathematik》1999,83(3):443-454
Summary. We prove that the 2-norm distance from an matrix A to the matrices that have a multiple eigenvalue is equal to where the singular values are ordered nonincreasingly. Therefore, the 2-norm distance from A to the set of matrices with multiple eigenvalues is
Received February 19, 1998 / Revised version received July 15, 1998 / Published online: July 7, 1999 相似文献
16.
Summary.
New approaches for computing tight lower
bounds to the eigenvalues of a class of
semibounded self-adjoint operators are
presented that require comparatively
little a priori spectral information and permit the
effective use of (among others) finite-element trial functions.
A variant of the method of intermediate problems making use
of operator decompositions having the form
is
reviewed and then developed into a new framework based on
recent inertia results in the Weinstein-Aronszajn theory. This
framework provides greater flexibility in analysis and permits
the formulation of a final computational task involving
sparse, well-structured matrices. Although our derivation is
based on an intermediate problem formulation, our results
may be specialized to obtain either the Temple-Lehmann
method or Weinberger's matrix method.
Received December 12, 1992 / Revised version
received October 5, 1994 相似文献
17.
Isabelle Gallagher 《Numerische Mathematik》2002,91(2):223-236
Summary. We show the consistency and the convergence of a spectral approximation of the bidimensional vorticity equation, proposed
by V. Zeitlin in[13] and studied numerically by I. Szunyogh, B. Kadar, and D. Dévényi in [12], whose main feature is that
it preserves the Hamiltonian structure of the vorticity equation.
Received February 22, 2000 / Revised version received October 23, 2000 / Published online June 20, 2001 相似文献
18.
Summary.
An explicit finite element method for numerically solving
the drift-diffusion semiconductor device equations in two space dimensions
is analyzed.
The method is based on the use of a mixed finite element method for the approximation
of the electric field and a discontinuous
upwinding finite element method for the approximation
of the electron and hole concentrations. The mixed method gives an approximate electric
field in the precise form needed by the discontinuous method, which is trivially
conservative and fully parallelizable. It is proven that the method produces
uniformly bounded concentrations and electric fields and that it converges
to the exact solution provided there is a convergent subsequence of the electron
concentrations. Numerical simulations are presented that display the
performance of the method and indicate the behavior of the solution.
Received
September 9, 1993 / Revised version received May 25,
1994 相似文献
19.
Summary. We examine a finite element approximation of a quasilinear boundary value elliptic problem in a three-dimensional bounded
convex domain with a smooth boundary. The domain is approximated by a polyhedron and a numerical integration is taken into
account. We apply linear tetrahedral finite elements and prove the convergence of approximate solutions on polyhedral domains
in the -norm to the true solution without any additional regularity assumptions.
Received May 23, 1997 / Published online December 6, 1999 相似文献
20.
Approximation theoretic results are obtained for approximation using continuous piecewise polynomials of degree p on meshes of triangular and quadrilateral elements. Estimates for the rate of convergence in Sobolev spaces , are given. The results are applied to estimate the rate of convergence when the p-version finite element method is used to approximate the -Laplacian. It is shown that the rate of convergence of the p-version is always at least that of the h-version (measured in terms of number of degrees of freedom used). If the solution is very smooth then the p-version attains an exponential rate of convergence. If the solution has certain types of singularity, the rate of convergence
of the p-version is twice that of the h-version. The analysis generalises the work of Babuska and others to the case . In addition, the approximation theoretic results find immediate application for some types of spectral and spectral element
methods.
Received August 2, 1995 / Revised version received January 26, 1998 相似文献