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1.
A monotone finite element scheme is obtained by applying the finite element method to the viscosity equation of the Hamilton-Jacobi equation on unstructured meshes. Under some constraints, we show that this scheme is monotone and its numerical solution converges to the viscosity solution of the Hamilton-Jacobi equa-tion. Numerical examples test the stability and the convergence of this scheme. 相似文献
2.
Summary. This work deals with the approximation of a time dependent variational inequality modelling the unilateral contact problem
of elastic-viscoplastic bodies in a bidimensional context. The problem is approximated in the space variable with nonconforming
finite element methods which allow the handling of nonmatching meshes on the contact zone. Several error estimates are established
and the corresponding numerical experiments are achieved.
Received Febuary 7, 2001 / Revised version received August 14, 2002 /
Published online October 29, 2002
Mathematics Subject Classification (1991): 73T05 相似文献
3.
Summary. Moving from the anisotropic interpolation error estimates derived in [12], we provide here both a-priori and a-posteriori
estimates for a generic elliptic problem. The a-priori result is deduced by following the standard finite element theory.
For the a-posteriori estimate, the analysis extends to anisotropic meshes the theory presented in [3–5]. Numerical test-cases
validate the derived results.
Received July 22, 2001 / Revised version received March 20, 2002 / Published online July 18, 2002
Mathematics Subject Classification (1991): 65N15, 65N50 相似文献
4.
Sándor Jenei 《Archive for Mathematical Logic》2003,42(5):489-514
We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical
characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard
algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows
from their other axioms.
Received: 7 January 2002 / Revised version: 4 April 2002 /
Published online: 19 December 2002
RID="*"
ID="*" Supported by the National Scientific Research Fund Hungary (OTKA F/032782).
Mathematics Subject Classification (2000): 20M14, 06F05
Key words or phrases: Residuated lattice – Conjunction for non-classical logics 相似文献
5.
This paper introduces an exact primal augmentation algorithm for solving general linear integer programs. The algorithm iteratively
substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine
inequalities. We prove that various versions of our algorithm are finite. It is a major concern in this paper to show how
the subproblem of replacing a column can be accomplished effectively. An implementation of the presented algorithms is given.
Computational results for a number of hard 0/1 integer programs from the MIPLIB demonstrate the practical power of the method.
Received: April 23, 2001 / Accepted: May 2002
Published online: March 21, 2003
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="#"
ID="#"Supported by a Gerhard-Hess-Preis and grant WE 1462 of the Deutsche Forschungsgemeinschaft, and by the European DONET
program TMR ERB FMRX-CT98-0202.
Mathematics Subject Classification (1991): 90C10 相似文献
6.
We prove versions of the Dual Ramsey Theorem and the Dual Ellentuck Theorem for families of partitions which are defined
in terms of games.
Received: 8 July 1999 Published online: 19 December 2002
RID="*"
ID="*" The author wishes to thank the Swiss National Science Foundation for supporting him.
The authors thank the referee for helpful comments.
Mathematics Subject Classification (2000): 03E02, 05D10, 03E35
Key words or phrases: Dual Ramsey Theorem – Dual Ellentuck Theorem – Partitions – Games 相似文献
7.
Minimizing risk models in stochastic shortest path problems 总被引:1,自引:0,他引:1
Yoshio Ohtsubo 《Mathematical Methods of Operations Research》2003,57(1):79-88
8.
Andrzej Rozkosz 《Probability Theory and Related Fields》2003,125(3):393-407
We extend the definition of solutions of backward stochastic differential equations to the case where the driving process
is a diffusion corresponding to symmetric uniformly elliptic divergence form operator. We show existence and uniqueness of
solutions of such equations under natural assumptions on the data and show its connections with solutions of semilinear parabolic
partial differential equations in Sobolev spaces.
Received: 22 January 2002 / Revised version: 10 September 2002 / Published online: 19 December 2002
Research supported by KBN Grant 0253 P03 2000 19.
Mathematics Subject Classification (2002): Primary 60H30; Secondary 35K55
Key words or phrases: Backward stochastic differential equation – Semilinear partial differential equation – Divergence form operator – Weak solution 相似文献
9.
10.
Imre Patyi 《Mathematische Annalen》2003,326(3):417-441
Let X be a complex Banach space with a countable unconditional basis, Ω⊂X pseudoconvex open, G a complex Banach Lie group. We show that a Runge–type approximation hypothesis on X, G (which we also prove for G a solvable Lie group) implies that any holomorphic cocycle on Ω with values in G can be resolved holomorphically if it can be resolved continuously.
Received: 1 March 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 32L05, 32E30, 46G20
RID="*"
ID="*" Kedves Szímuskának.
RID="*"
ID="*" To my dear Wife. 相似文献
11.
Andreas Fischer 《Mathematical Programming》2002,94(1):91-124
An iterative framework for solving generalized equations with nonisolated solutions is presented. For generalized equations
with the structure , where is a multifunction and F is single-valued, the framework covers methods that, at each step, solve subproblems of the type . The multifunction approximates F around s. Besides a condition on the quality of this approximation, two other basic assumptions are employed to show Q-superlinear
or Q-quadratic convergence of the iterates to a solution. A key assumption is the upper Lipschitz-continuity of the solution
set map of the perturbed generalized equation . Moreover, the solvability of the subproblems is required. Conditions that ensure these assumptions are discussed in general
and by means of several applications. They include monotone mixed complementarity problems, Karush-Kuhn-Tucker systems arising
from nonlinear programs, and nonlinear equations. Particular results deal with error bounds and upper Lipschitz-continuity
properties for these problems.
Received: November 2001 / Accepted: November 2002 Published online: December 9, 2002
Key Words. generalized equation – nonisolated solutions – Newton's method – superlinear convergence – upper Lipschitz-continuity – mixed
complementarity problem – error bounds
Mathematics Subject Classification (1991): 90C30, 65K05, 90C31, 90C33 相似文献
12.
Perfectly matched layers in 1-d : energy decay for continuous and semi-discrete waves 总被引:2,自引:1,他引:1
In this paper we investigate the efficiency of the method of perfectly matched layers (PML) for the 1-d wave equation. The
PML method furnishes a way to compute solutions of the wave equation for exterior problems in a finite computational domain
by adding a damping term on the matched layer. In view of the properties of solutions in the whole free space, one expects
the energy of solutions obtained by the PML method to tend to zero as t → ∞, and the rate of decay can be understood as a measure of the efficiency of the method. We prove, indeed, that the exponential
decay holds and characterize the exponential decay rate in terms of the parameters and damping potentials entering in the
implementation of the PML method. We also consider a space semi-discrete numerical approximation scheme and we prove that,
due to the high frequency spurious numerical solutions, the decay rate fails to be uniform as the mesh size parameter h tends to zero. We show however that adding a numerical viscosity term allows us to recover the property of exponential decay
of the energy uniformly on h. Although our analysis is restricted to finite differences in 1-d, most of the methods and results apply to finite elements
on regular meshes and to multi-dimensional problems.
This work started while the first author was visiting the Department of Mathematics of the Universidad Autónoma de Madrid,
in the frame of the European program “New materials, adaptive systems and their nonlinearities: modeling, control and numerical
simulation” HPRN-CT-2002-00284. The work was finished while both authors visited the Isaac Newton Institute of Cambridge within
the Program “Highly Oscillatory Problems”. 相似文献
13.
This paper presents a renormalization and homogenization theory for fractional-in-space or in-time diffusion equations with
singular random initial conditions. The spectral representations for the solutions of these equations are provided. Gaussian
and non-Gaussian limiting distributions of the renormalized solutions of these equations are then described in terms of multiple
stochastic integral representations.
Received: 30 May 2000 / Revised version: 9 November 2001 / Published online: 10 September 2002
Mathematics Subject Classification (2000): Primary 62M40, 62M15; Secondary 60H05, 60G60
Key words or phrases: Fractional diffusion equation – Scaling laws – Renormalised solution – Long-range dependence – Non-Gaussian scenario – Mittag-Leffler
function – Stable distributions – Bessel potential – Riesz potential 相似文献
14.
Peter K. Moore 《Numerische Mathematik》2003,94(2):367-401
Summary. Hp-adaptive finite element codes require methods for estimating the error at several spatial orders and for interpolating solutions
between grids. Lobatto polynomial-based techniques are presented for both. An interpolation error-based error estimation strategy
for a posteriori error estimates is generalized to yield asymptotically exact error estimates one order higher than the computed solution.
The estimates involve high-order derivatives of the solution that must be approximated from the computed solution. Differentiating
a ``Taylor-like' series for error in the Lobatto interpolant and using the weak form of the equations yields the correct
derivative approximations. This leads to a more robust order selection strategy. Interpolation between grids is done over
each element using the Lobatto interpolating polynomial. Explicit formulas for the inverse of the resulting Lobatto interpolation
matrices are given. Computational results illustrate the theory.
Received June 25, 2001 / Revised version received February 12, 2002 / Published online October 29, 2002
Mathematics Subject Classification (1991): 65M15,65M20,65M60
This research was partially supported by NSF Grant #DMS-0196108. 相似文献
15.
16.
Ikuo Yoneda 《Archive for Mathematical Logic》2003,42(5):423-433
We show that any relational generic structure whose theory has finite closure and amalgamation over closed sets is stable
CM-trivial with weak elimination of imaginaries.
Received: 21 December 2001 /
Published online: 5 November 2002
Mathematics Subject Classification (2000): 03C45
Key words or phrases: CM-triviality – Generic structures – Stability 相似文献
17.
Wensheng Wang 《Probability Theory and Related Fields》2003,126(2):203-220
Kesten and Spitzer have shown that certain random walks in random sceneries converge to stable processes in random sceneries.
In this paper, we consider certain random walks in sceneries defined using stationary Gaussian sequence, and show their convergence
towards a certain self-similar process that we call fractional Brownian motion in Brownian scenery.
Received: 17 April 2002 / Revised version: 11 October 2002 /
Published online: 15 April 2003
Research supported by NSFC (10131040).
Mathematics Subject Classification (2002): 60J55, 60J15, 60J65
Key words or phrases: Weak convergence – Random walk in random scenery – Local time – Fractional Brownian motion in Brownian scenery 相似文献
18.
Summary. We analyze mixed hp-discontinuous Galerkin finite element methods (DGFEM) for Stokes flow in polygonal domains. In conjunction with geometrically refined quadrilateral meshes and linearly increasing approximation orders, we prove that the hp-DGFEM leads to exponential rates of convergence for piecewise analytic solutions exhibiting singularities near corners.
Mathematics Subject Classification (2000):65N30 相似文献
19.
Summary. When a system of linear equations is ill-conditioned, regularization techniques provide a quite useful tool for trying to
overcome the numerical inherent difficulties: the ill-conditioned system is replaced by another one whose solution depends
on a regularization term formed by a scalar and a matrix which are to be chosen. In this paper, we consider the case of several
regularizations terms added simultaneously, thus overcoming the problem of the best choice of the regularization matrix. The
error of this procedure is analyzed and numerical results prove its efficiency.
Received January 15, 2002 / Revised version received July 31, 2002 / Published online October 29, 2002
Mathematics Subject Classification (1991): 65F05 – 65F22 相似文献