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991.
Mireille Bossy Jean-François Jabir 《Stochastic Processes and their Applications》2011,121(12):2751-2775
We construct a confined Langevin type process aimed to satisfy a mean no-permeability condition at the boundary. This Langevin process lies in the class of conditional McKean Lagrangian stochastic models studied by Bossy, Jabir and Talay (2010) [5]. The confined process considered here is a first construction of solutions to the class of Lagrangian stochastic equations with boundary condition issued by the so-called PDF methods for Computational Fluid Dynamics. We prove the well-posedness of the confined system when the state space of the Langevin process is a half-space. 相似文献
992.
An optimization approach for the determination of open boundary conditions for Computational Fluid Dynamics is introduced, whereas the error between the solution σ and interior observations ω is minimized. The numerical weather prediction (NWP) model ALADIN–Austria provides data of wind speed and wind direction at virtual weather stations within the area of interest. Also, data from real weather stations and other sources can be incorporated into the model, respectively. In this work, the optimization method is applied to the constant density Navier–Stokes Equations. Thereby, for stabilizing the ill-posed pseudo inverse problem several regularization methods are reviewed. Further, numerical studies are carried out to identify the supreme regularization method for the presented application. Finally, the algorithm is applied to the micro- and meso-scale flow over the Grimming mountain, Austria. The results are compared with real weather station data and show suitable correlation with the measurements. 相似文献
993.
In this paper, we construct the exact solution for fluid motion caused by the uniform expansion of a cylindrical or spherical piston into still air. Following Lighthill [1], we introduce velocity potential into the analysis and seek a similarity form of the solution. We find both numerical and analytic solutions of the second order nonlinear differential equation, with the boundary conditions at the shock and at the piston. The results obtained from the analytic solutions justify numerical solution and the approximate solution of Lighthill [1]. We find that although the approximate solution of Lighthill [1] gives remarkably good numerical results, the analytic form of that solution is not mathematically satisfactory. We also find that in case of spherical piston motion Lighthill’s [1] solution differs significantly from that of our analytic and numerical solutions. We use Pade′ approximation to extend the radius of convergence of the series solution. We also carry out some local analysis at the boundary to obtain some singular solutions. 相似文献
994.
Alexander Gladkov Mohammed Guedda 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(13):4573-4580
In this paper we consider a semilinear parabolic equation ut=Δu−c(x,t)up for (x,t)∈Ω×(0,∞) with nonlinear and nonlocal boundary condition u∣∂Ω×(0,∞)=∫Ωk(x,y,t)uldy and nonnegative initial data where p>0 and l>0. We prove some global existence results. Criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given. 相似文献
995.
996.
In this paper, we consider the pressure projection stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality problem of the second kind with the Stokes operator. The H1 and L2 error estimates for the velocity and the L2 error estimate for the pressure are obtained. Finally, the numerical results are displayed to verify the theoretical analysis. 相似文献
997.
S.A. Yousefi 《Journal of Computational and Applied Mathematics》2011,235(17):5272-5283
Some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications. In this paper, a numerical method which employs the Bernstein polynomials basis is implemented to give the approximate solution of a parabolic partial differential equation with boundary integral conditions. The properties of Bernstein polynomials, and the operational matrices for integration, differentiation and the product are introduced and are utilized to reduce the solution of the given parabolic partial differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new technique. 相似文献
998.
István Faragó Róbert Horváth Sergey Korotov 《Numerical Methods for Partial Differential Equations》2011,27(3):702-720
In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion‐reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
999.
O. Chkadua S.E. Mikhailov D. Natroshvili 《Numerical Methods for Partial Differential Equations》2011,27(1):121-140
Segregated direct boundary‐domain integral equation (BDIE) systems associated with mixed, Dirichlet and Neumann boundary value problems (BVPs) for a scalar “Laplace” PDE with variable coefficient are formulated and analyzed for domains with interior cuts (cracks). The main results established in the paper are the BDIE equivalence to the original BVPs and invertibility of the BDIE operators in the corresponding Sobolev spaces. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
1000.
应用Avery-Peterson不动点定理,讨论了带p-Laplacian算子的三阶三点边值问题,当非线性项f满足一定增长条件时,得到了上述边值问题至少存在三个正解的充分条件. 相似文献