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71.
In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order CrouzeixRaviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis. 相似文献
72.
We investigate the long time behaviour of the L2-energy of solutions to wave equations with variable speed of propagation. The novelty of the approach is the combination of estimates for higher order derivatives of the coefficient with a stabilisation property. 相似文献
73.
The authors prove a new Carleman estimate for general linear second order parabolic equation with nonhomogeneous boundary conditions. On the basis of this estimate, improved Carleman estimates for the Stokes system and for a system of parabolic equations with a penalty term are obtained. This system can be viewed as an approximation of the Stokes system. 相似文献
74.
In this paper, we prove the global existence and asymptotic behavior, as time tends to infinity, of solutions in Hi (i=1, 2) to the initial boundary value problem of the compressible Navier–Stokes equations of one‐dimensional motion of a viscous heat‐conducting gas in a bounded region with a non‐autonomous external force and a heat source. Some new ideas and more delicate estimates are used to prove these results. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
75.
Irena Pawłow Wojciech M. Zaja̧czkowski 《Mathematical Methods in the Applied Sciences》2009,32(17):2197-2242
In this paper we prove the existence and uniqueness of a global in time, regular solution to the Cahn–Hilliard system coupled with viscoelasticity. The system arises as a model, regularized by a viscous damping, of phase separation process in a binary deformable alloy quenched below a critical temperature. The key tools in the analysis are estimates of absorbing type with the property of exponentially time‐decreasing contribution of the initial data. Such estimates allow not only to prolong the solution step by step on the infinite time interval but also to conclude the existence of an absorbing set. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
76.
In this paper, the Cauchy problem for the Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a modified regularization method to solve it based on the solution given by the method of separation of variables. Convergence estimates are presented under two different a-priori bounded assumptions for the exact solution. Finally, numerical examples are given to show the effectiveness of the proposed numerical method. 相似文献
77.
Jérôme Vétois 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):3881-3905
We prove universal, pointwise, a priori estimates for nonnegative solutions of anisotropic nonlinear elliptic equations. 相似文献
78.
Matthew D. Blair Hart F. Smith Christopher D. Sogge 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(5):1817-1829
We prove certain mixed-norm Strichartz estimates on manifolds with boundary. Using them we are able to prove new results for the critical and subcritical wave equation in 4-dimensions with Dirichlet or Neumann boundary conditions. We obtain global existence in the subcritical case, as well as global existence for the critical equation with small data. We also can use our Strichartz estimates to prove scattering results for the critical wave equation with Dirichlet boundary conditions in 3-dimensions. 相似文献
79.
Kassem Mustapha 《Journal of Computational and Applied Mathematics》2009,231(2):735-744
In this paper we study the numerical solution of an initial value problem of a sub-diffusion type. For the time discretization we apply the discontinuous Galerkin method and we use continuous piecewise finite elements for the space discretization. Optimal order convergence rates of our numerical solution have been shown. We compare our theoretical error bounds with the results of numerical computations. We also present some numerical results showing the super-convergence rates of the proposed method. 相似文献
80.
Solving the Vlasov–Maxwell problem can lead to very expensive computations. To construct a simpler model, Laval et al. [G. Laval, S. Mas-Gallic, P.A. Raviart, Paraxial approximation of ultrarelativistic intense beams, Numer. Math. 69 (1) (1994) 33–60] proposed to exploit the paraxial property of the charged particle beams, i.e the property that the particles of the beam remain close to an optical axis. They so constructed a paraxial model and performed its mathematical analysis. In this paper, we investigate how their framework can be adapted to handle the axisymmetric geometry, and its coupling with the Vlasov equation. First, one constructs numerical schemes and error estimates results for this discretization are reported. Then, a Particle In Cell (PIC) method, in the case of highly relativistic beams is proposed. Finally, numerical results are given. In particular, numerical comparisons with the Vlasov–Poisson model illustrate the possibilities of this approach. 相似文献