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21.
Olivier Baconneau Alessandra Lunardi 《Transactions of the American Mathematical Society》2004,356(3):987-1005
We establish existence, uniqueness, and regularity results for solutions to a class of free boundary parabolic problems, including the free boundary heat equation which arises in the so-called ``focusing problem' in the mathematical theory of combustion. Such solutions are proved to be smooth with respect to time for positive , if the data are smooth.
22.
We solve a linear parabolic equation in d , d 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes. 相似文献
23.
24.
In order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
25.
The (all-terminal) reliability of a graph G is the probability that all vertices are in the same connected component, given that vertices are always operational but edges fail independently each with probability p. Computing reliability is #P-complete, and hence is expected to be intractable. Consequently techniques for efficiently (and effectively) bounding reliability have been the major thrust of research in the area. We utilize a deep connection between reliability and chip firings on graphs to improve previous bounds for reliability. 相似文献
26.
This paper considers a posteriori error estimates by averaged gradients in second order parabolic problems. Fully discrete
schemes are treated. The theory from the elliptic case as to when such estimates are asymptotically exact, on an element,
is carried over to the error on an element at a given time. The basic principle is that the elliptic theory can be extended
to the parabolic problems provided the time-step error is smaller than the space-discretization error. Numerical illustrations
confirming the theoretical results are given. Our results are not practical in the sense that various constants can not be
estimated realistically. They are conceptual in nature.
AMS subject classification (2000) 65M60, 65M20, 65M15 相似文献
27.
周艳杰 《数学的实践与认识》2008,38(15)
在已有的对CVD化学方程半离散化和全离散化混合有限元解的存在性及其误差分析的基础上,对其全离散化混合有限元解进行了数值模拟,结果进一步表明了混合有限元解的高精度、易于计算的良好性质. 相似文献
28.
A microscopic cluster model with a fully correlated Gaussian basis is developed. In the model, the stochastic variational method is used in order to calculate the ground-energy and the mean-square radius conveniently. Based on this model, the ground-energy level and radius of the neutron halo nucleus, 6He, are calculated as a α+n+n three-cluster model. The results are in good agreement with the experimental data. 相似文献
29.
Erhan Bayraktar Arash Fahim 《Numerical Methods for Partial Differential Equations》2014,30(3):902-929
We present a stochastic numerical method for solving fully nonlinear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the nonlinearity. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 902–929, 2014 相似文献
30.
This paper addresses an application of ORTHOMIN and GMRES to petroleum reservoir simulation using the black oil model on unstructured grids. Comparisons between these two algorithms are presented in terms of storage and total flops per restart step. Numerical results indicate that GMRES is faster than ORTHOMIN for all tested petroleum reservoir problems, particularly for large scale problems. The control volume function approximation method is utilized in the discretization of the governing equations of the black oil model. This method can accurately approximate both the pressure and velocity in the simulation of multiphase flow in porous media, effectively reduce grid orientation effects, and be easily applied to arbitrarily shaped control volumes. It is particularly suitable for hybrid grid reservoir simulation. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献