共查询到20条相似文献,搜索用时 343 毫秒
1.
Rodolfo Bermejo 《Numerische Mathematik》2001,87(4):597-623
Summary. We analyze in the norm a class of semi-Lagrangian advective schemes introduced by the author and A. Staniforth in 1992 to improve the solution
produced by numerical models for weather prediction and climate studies that use semi-Lagrangian advective schemes. The new
quasi-monotone and conservative semi-Lagrangian schemes are stable and converge optimally when the solution is sufficiently smooth.
Received May 17, 1999 / Revised version received November 22, 1999 / Published online August 24, 2000 相似文献
2.
On one approach to a posteriori error estimates for evolution problems solved by the method of lines 总被引:2,自引:0,他引:2
Summary. In this paper, we describe a new technique for a posteriori error estimates suitable to parabolic and hyperbolic equations
solved by the method of lines. One of our goals is to apply known estimates derived for elliptic problems to evolution equations.
We apply the new technique to three distinct problems: a general nonlinear parabolic problem with a strongly monotonic elliptic
operator, a linear nonstationary convection-diffusion problem, and a linear second order hyperbolic problem. The error is
measured with the aid of the -norm in the space-time cylinder combined with a special time-weighted energy norm. Theory as well as computational results
are presented.
Received September 2, 1999 / Revised version received March 6, 2000 / Published online March 20, 2001 相似文献
3.
Summary. We investigate the convergence of difference schemes for the one-dimensional heat equation when the coefficient at the time
derivative (heat capacity) is represents the magnitude of the heat capacity concentrated at the point . An abstract operator method is developed for analyzing this equation. Estimates for the rate of convergence in special discrete
energetic Sobolev's norms, compatible with the smoothness of the solution are obtained.
Received November 2, 1999 / Revised version received July 24, 2000 / Published online May 4, 2001 相似文献
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5.
K. Segeth 《Numerische Mathematik》1999,83(3):455-475
Summary. Convergence of a posteriori error estimates to the true error for the semidiscrete finite element method of lines is shown
for a nonlinear parabolic initial-boundary value problem.
Received June 15, 1997 / Revised version received May 15, 1998 / Published online: June 29, 1999 相似文献
6.
7.
J.-F. Gerbeau 《Numerische Mathematik》2000,87(1):83-111
Summary. We propose and analyze a stabilized finite element method for the incompressible magnetohydrodynamic equations. The numerical
results that we present show a good behavior of our approximation in experiments which are relevant from an industrial viewpoint.
We explain in particular in the proof of our convergence theorem why it may be interesting to stabilize the magnetic equation
as soon as the hydrodynamic diffusion is small and even if the magnetic diffusion is large. This observation is confirmed
by our numerical tests.
Received August 31, 1998 / Revised version received June 16, 1999 / Published online June 21, 2000 相似文献
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10.
Summary. We present an approximate-inertial-manifold-based postprocess to enhance Chebyshev or Legendre spectral Galerkin methods.
We prove that the postprocess improves the order of convergence of the Galerkin solution, yielding the same accuracy as the
nonlinear Galerkin method. Numerical experiments show that the new method is computationally more efficient than Galerkin
and nonlinear Galerkin methods. New approximation results for Chebyshev polynomials are presented.
Received January 5, 1998 / Revised version received September 7, 1999 / Published online June 8, 2000 相似文献
11.
12.
Some applications of impulse control in mathematical finance 总被引:5,自引:0,他引:5
Ralf Korn 《Mathematical Methods of Operations Research》1999,50(3):493-518
13.
Summary. We consider a piecewise constant finite element approximation to the convolution Volterra equation problem of the second
kind: find such that in a time interval . An a posteriori estimate of the error measured in the norm is developed and used to provide a time step selection criterion for an adaptive solution algorithm. Numerical examples
are given for problems in which is of a form typical in viscoelasticity theory.
Received March 5, 1998 / Revised version received November 30, 1998 / Published online December 6, 1999 相似文献
14.
Summary. We introduce two classes of monotone finite volume schemes for Hamilton-Jacobi equations. The corresponding approximating
functions are piecewise linear defined on a mesh consisting of triangles. The schemes are shown to converge to the viscosity
solution of the Hamilton–Jacobi equation.
Received February 25, 1998 / Published online: June 29, 1999 相似文献
15.
We consider the M/G/1 and GI/M/1 types of Markov chains for which their one step transitions depend on the times of the transitions.
These types of Markov chains are encountered in several stochastic models, including queueing systems, dams, inventory systems,
insurance risk models, etc. We show that for the cases when the time parameters are periodic the systems can be analyzed using
some extensions of known results in the matrix-analytic methods literature. We have limited our examples to those relating
to queueing systems to allow us a focus. An example application of the model to a real life problem is presented. 相似文献
16.
Summary. This paper is devoted to both theoretical and numerical study of a system involving an eikonal equation of Hamilton-Jacobi
type and a linear conservation law as it comes out of the geometrical optics expansion of the wave equation or the semiclassical
limit for the Schr?dinger equation. We first state an existence and uniqueness result in the framework of viscosity and duality
solutions. Then we study the behavior of some classical numerical schemes on this problem and we give sufficient conditions
to ensure convergence. As an illustration, some practical computations are provided.
Received December 6, 1999 / Revised version received August 2, 2000 / Published online June 7, 2001 相似文献
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18.
Nikolai Yu. Bakaev 《Numerische Mathematik》2002,92(4):621-651
Summary. We consider fully discrete approximations to a parabolic initial-boundary value problem with rough or distribution-valued
initial data in two space dimensions. For discretization in time and space, we apply single step methods and the standard
Galerkin method with piecewise linear test functions, respectively. For spatial discretization of the initial condition, we
are however forced to use more involved constructions. Our main result is stability and error estimates of the discrete solutions.
Received October 21, 1999 / Revised version received May 3, 2001 / Published online December 18, 2001 相似文献
19.
A posteriori error estimate for finite volume approximations to singularly perturbed nonlinear convection-diffusion equations 总被引:1,自引:0,他引:1
Mario Ohlberger 《Numerische Mathematik》2001,87(4):737-761
Summary. This paper is devoted to the study of a posteriori and a priori error estimates for the scalar nonlinear convection diffusion equation . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived
in the -norm in the situation, where the diffusion parameter is smaller or comparable to the mesh size. Numerical experiments underline the theoretical results.
Received February 25, 1999 / Revised version received July 6, 1999 / Published online August 2, 2000 相似文献
20.
Jae Ryong Kweon 《Numerische Mathematik》2000,86(2):305-318
Summary. We formulate the compressible Stokes system given in (1.1) into a (new) weak formulation (2.1). A finite element method for
this is presented. Existence and uniqueness of the finite element method is shown. An optimal error estimate for the numerical
approximation is obtained. Numerical examples are given, showing its efficiency and rates of convergence of the approximate
solutions that results from the discrete problem (3.1).
Received October 20, 1996 / Revised version received January 21, 1999 / Published online: April 20, 2000 相似文献