共查询到20条相似文献,搜索用时 0 毫秒
1.
G. F. Carey B. N. Jiang R. Showalter 《Numerical Methods for Partial Differential Equations》1988,4(3):165-171
A regularization procedure for nonlinear conservation equations is introduced and demonstrated to have a stabilizing effect on the numerical solution of the associated approximate problem. Representative results for a least-squares finite-element method are given, and the numerical performance of the stabilization procedure explored. The effect of the regularization term is similar to a local numerical dissipation dependent on the numerical itegration time step. 相似文献
2.
Free surface flow is one of the most difficult problems in engineering to be solved, since velocity and pressure fields depend on the free surface. On the other hand, the position of the free surface is unknown previously. Furthermore, the boundary condition on the free surface is expressed by a complicated equation. In an alluvial stream, where the boundaries of the domain are not fixed, addition of free surface at the bed will increase this difficulty. A domain mapping technique is developed in this paper to study the bed evolutions. The flow is considered 2D, choosing two coordinates in streamwise and upward directions. With a proper transformation, the hydrodynamics and sediment transport governing equations in irregular domain will be mapped into a simple rectangular one. The new domain can be discretize by finite elements. The transformed governing equations are solved to obtain desired variables in the mapped domain. With a proper transformation, there is no need of inverse mapping to obtain the free water surface profile and bedform evolution and migration in the actual domain. The model has been applied to streams with movable bed and the results show a good agreement with the experimental experiences. 相似文献
3.
4.
Konrad Schmüdgen 《Mathematische Zeitschrift》2006,254(3):641-653
Let G be a connected and simply connected real Lie group with Lie algebra
. Semialgebraic subsets of the unitary dual of G are defined and a strict Positivstellensatz for positive elements of the universal enveloping algebra
of
is proved.
An erratum to this article is available at . 相似文献
5.
The combination technique for a two-dimensional convection-diffusion problem with exponential layers
Sebastian Franz Fang Liu Hans-Görg Roos Martin Stynes Aihui Zhou 《Applications of Mathematics》2009,54(3):203-223
Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a
sparse grid Galerkin finite element method with Shishkin meshes. Writing N for the maximum number of mesh intervals in each
coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin
FEM on and meshes. It is shown that the combination FEM yields (up to a factor ln N) the same order of accuracy in the associated energy norm as the Galerkin FEM on an N × N mesh, but it requires only (N
3/2) degrees of freedom compared with the (N
2) used by the Galerkin FEM. An analogous result is also proved for the streamline diffusion finite element method.
This work was supported by the National Natural Science Foundation of China (10701083 and 10425105), the Chinese National
Basic Research Program (2005CB321704) and the Boole Centre for Research in Informatics at National University of Ireland Cork. 相似文献
6.
A discrete assimilation system for a one-dimensional variable coefficient convection-diffusion equation is constructed. The variational adjoint method combined with the regularization technique is employed to retrieve the initial condition and diffusion coefficient with the aid of a set of simulated observations. Several numerical experiments are performed: (a) retrieving both the initial condition and diffusion coefficient jointly (Experiment JR), (b) retrieving either of them separately (Experiment SR), (c) retrieving only the diffusion coefficient with the iteration count increased to 800 (Experiment NoR-SR), and (d) retrieving only the diffusion coefficient with the consideration of a regularization term based on the Experiment NoR-SR (Experiment AdR-SR). The results indicate that within the limit of 100 iterations, the retrieval quality of the Experiment SR is better than those from the Experiment JR. Compared with the initial condition, the diffusion coefficient is a little difficult to retrieve, whereas we still achieve the desired result by increasing the iterations or integrating the regularization term into the cost functional for the improvement with respect to the diffusion coefficient. Further comparisons between the Experiment NoR-SR and AdR-SR show that the regularization term can really help not only improve the precision of retrieval to a large extent, but also speed up the convergence of solution, even if some perturbations are imposed on those observations. 相似文献
7.
R. Verfürth 《Numerische Mathematik》1998,80(4):641-663
Summary. We derive a posteriori error estimators for convection-diffusion equations with dominant convection. The estimators yield
global upper and local lower bounds on the error measured in the energy norm such that the ratio of the upper and lower bounds
only depends on the local mesh-Peclet number. The estimators are either based on the evaluation of local residuals or on the
solution of discrete local Dirichlet or Neumann problems.
Received February 10, 1997 / Revised version received November 4, 1997 相似文献
8.
Lina Hemmingsson 《Numerische Mathematik》1998,81(2):211-248
In this paper we define and analyze a semi-circulant preconditioner for the convection-diffusion equation. We derive analytical
formulas for the eigenvalues and the eigenvectors of the preconditioned system of equations. We show that for mesh Péclet
numbers less than 2, the rate of convergence depends only on the mesh Péclet number and the direction of the convective field and not on the spatial grid ratio or the number of unknowns.
Received February 20, 1997 / Revised version received November 19, 1997 相似文献
9.
A. I. Ovchinnikov 《Journal of Mathematical Sciences》2006,135(5):3355-3362
We construct sections of a differential spectrum using only localization and projective limits. For this purpose we introduce
a special form of multiplicative systems generated by one differential polynomial and call it D-localization. Owing to this technique one can construct sections of a differential spectrum of a differential ring
without computation of diffspec
. We compare our construction with Kovacic’s structure sheaf and with the results obtained by Keigher [J. Pure Appl. Algebra,
27, 163–172 (1983)]. We show how to compute sections of factor-rings of rings of differential polynomials. All computations
in this paper are factorization-free.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 133–144, 2003. 相似文献
10.
In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut=J∗u−u+G∗(f(u))−f(u) in Rd, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equation ut=Δu+b⋅∇(f(u)). In fact, we prove that solutions of the nonlocal equation converge to the solution of the usual convection-diffusion equation when we rescale the convolution kernels J and G appropriately. Finally we study the asymptotic behaviour of solutions as t→∞ when f(u)=|u|q−1u with q>1. We find the decay rate and the first-order term in the asymptotic regime. 相似文献
11.
A simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection-diffusion problems in any spatial dimension by properly averaging the PDE coefficients on element edges. The resulting finite element stiffness matrix is an -matrix under some mild assumption for the underlying (generally unstructured) finite element grids. As a consequence the proposed edge-averaged finite element scheme is particularly interesting for the discretization of convection dominated problems. This scheme admits a simple variational formulation, it is easy to analyze, and it is also suitable for problems with a relatively smooth flux variable. Some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems.
12.
Wolfgang Soergel 《Mathematische Zeitschrift》1990,204(1):559-581
Written during the author's stay at MSRI, supported by a Stipendium der Clemens Plassmann Stiftung 相似文献
13.
利用在网格内恰当选取特征线上插值点的技巧,提出了一种新型的求解对流扩散方程的特征差分方法,并给出了稳定性与收敛性分析.该方法避免了数值扩散的产生,同时具有O(τ h~2)阶的收敛阶.数值实验表明,该方法是一个高效、稳定和收敛的数值方法. 相似文献
14.
In this paper, a new DG method was designed to solve the model problem of the one-dimensional singularly-perturbed convection-diffusion equation. With some special chosen numerical traces, the existence and uniqueness of the DG solution is provided. The superconvergent points inside each element are observed. Particularly, the 2p + 1-order superconvergence and even uniform superconvergence under layer-adapted mesh are observed numerically. 相似文献
15.
Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems 总被引:1,自引:0,他引:1
Summary. We analyze nonconforming finite element approximations of streamline-diffusion type for solving convection-diffusion problems.
Both the theoretical and numerical investigations show that additional jump terms have to be added in the nonconforming case
in order to get the same order of convergence in L as in the conforming case for convection dominated problems. A rigorous error analysis supported by numerical experiments
is given.
Received June 26, 1996 / Revised version received November 20, 1996 相似文献
16.
Summary. A new characteristic finite element scheme is presented for It is of second order accuracy in time increment, symmetric,
and unconditionally stable. Optimal error estimates are proved in the framework of -theory. Numerical results are presented for two examples, which show the advantage of the scheme.
Received November 22, 2000 / Revised version received July 11, 2001 / Published online October 17, 2001 相似文献
17.
The object of this paper is to show that many of the known results concerning the structure of semiperfect FPF rings can be extended to a larger class of FPF rings. The main attributes of this larger class of rings are they have enough principle idempo-tents and idempotents lift modulo the Jacobson radical. We call these rings epi-semiperfect rings. 相似文献
18.
A new characteristic finite difference method for solving the two-sided space-fractional convection-diffusion equations is presented, by combining characteristic methods and fractional finite difference methods. Stability, consistency and (therefore) convergence of the new method are discussed in this paper. An error estimate is given. Numerical experiments of this method are carried out and compared with other known methods. 相似文献
19.
20.
Georgia Benkart Seok-Jin Kang Duncan Melville 《Transactions of the American Mathematical Society》1998,350(8):3297-3319
We construct quantum deformations of enveloping algebras of Borcherds superalgebras, their Verma modules, and their irreducible highest weight modules.