共查询到20条相似文献,搜索用时 62 毫秒
1.
Xiaoyang Zheng Xiaofan YangHong Su Liqiong Qiu 《Applied mathematics and computation》2011,218(7):3002-3018
By incorporating the Legendre multiwavelet into the discontinuous Galerkin (DG) method, this paper presents a novel approach for solving Poisson’s equation with Dirichlet boundary, which is known as the discontinuous Legendre multiwavelet element (DLWE) method, derive an adaptive algorithm for the method, and estimate the approximating error of its numerical fluxes. One striking advantage of our method is that the differential operator, boundary conditions and numerical fluxes involved in the elementwise computation can be done with lower time cost. Numerical experiments demonstrate the validity of this method. Furthermore, this paper generalizes the DLWE method to the general elliptic equations defined on a bounded domain and describes the possibilities of constructing optimal adaptive algorithm. The proposed method and its generalizations are also applicable to some other kinds of partial differential equations. 相似文献
2.
Mario Annunziato & Eleonora Messina 《计算数学(英文版)》2019,37(1):33-47
We study a numerical method for solving a system of Volterra-renewal integral equations
with space fluxes, that represents the Chapman-Kolmogorov equation for a class of
piecewise deterministic stochastic processes. The solution of this equation is related to
the time dependent distribution function of the stochastic process and it is a non-negative
and non-decreasing function of the space. Based on the Bernstein polynomials, we build
up and prove a non-negative and non-decreasing numerical method to solve that equation,
with quadratic convergence order in space. 相似文献
3.
Xue-Cheng Tai 《Numerical Methods for Partial Differential Equations》1998,14(1):27-46
A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank–Nicolson scheme is used for the parabolic equation, then by suitably choosing the space decomposition, only O(| log τ |) steps of iteration at each time level are needed, where τ is the time-step size. Applications to overlapping domain decomposition and to a two-level method are given for a second-order parabolic equation. The analysis shows that only a one-element overlap is needed. Discussions about iterative and noniterative methods for parabolic equations are presented. A method that combines the two approaches and utilizes some of the good properties of the two approaches is tested numerically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 27–46, 1998 相似文献
4.
Ricerche di Matematica - The Boltzmann equation for charge transport in monolayer graphene is numerically solved by using a discontinuous Galerkin method. The numerical fluxes are based on a... 相似文献
5.
Pierre Degond Stphane Gnieys Ansgar Jüngel 《Mathematical Methods in the Applied Sciences》1998,21(15):1399-1413
The steady-state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet–Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot be expected for physical reasons. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd. 相似文献
6.
Petr N. Vabishchevich 《BIT Numerical Mathematics》2013,53(3):755-778
Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of heat fluxes. In this case, the mathematical model is based on a hyperbolic equation of second order or a system of equations for the temperature and heat fluxes. In this paper we construct for the hyperbolic heat conduction equation the additive schemes of splitting with respect to directions. Unconditional stability of locally one-dimensional splitting schemes is established. New splitting schemes are proposed and studied for a system of equations written in terms of the temperature and heat fluxes. 相似文献
7.
Gunilla Efraimsson 《Numerical Methods for Partial Differential Equations》1998,14(3):353-365
We introduce a method, constructed such that numerical solutions of the wave equation are well behaved when the solutions also contain discontinuities. The wave equation serves as a model problem for the Euler equations when the solution contains a contact discontinuity. Numerical computations of linear equations and the Euler equations in one and two dimensions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 353–365, 1998 相似文献
8.
A splitting of a third order partial differential equation into a first-order and a second-order one is proposed as the basis for a mixed finite element method to approximate its solution. A time-continuous numerical method is described and error estimates for its solution are demonstrated. Finally, a full discretization is described based on backward Euler finite differences in time, and error estimates for the resulting approximation are established. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 89–96, 1998 相似文献
9.
Murli M. Gupta Jules Kouatchou 《Numerical Methods for Partial Differential Equations》1998,14(5):593-606
A symbolic procedure for deriving various finite difference approximations for the three-dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation local solutions of the differential equation and obtain the standard second-order scheme (7-point), three fourth-order finite difference schemes (15-point, 19-point, 21-point), and one sixth-order scheme (27-point). The symbolic method is simple and can be used to obtain the finite difference approximations for other partial differential equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 593–606, 1998 相似文献
10.
In this article, local unique continuation on a line for solutions of the Helmholtz equation is discussed. The fundamental solution of the exterior problem for the Helmholtz equation have a logarithmic singularity which behaves similar to those of the interior problem for the Laplace equation in two dimension. A Hölder-type conditional stability estimate of the proposed exterior problem for the Helmholtz equation is obtained by adopting the complex extension method in Cheng and Yamamoto [J. Cheng and M. Yamamoto, Unique continuation on a line for harmonic functions, Inverse Probl. 14 (1998), pp. 869–882]. Finally, a regularization scheme based on the collocation method is compatible with the Hölder-type stability estimate provided that the line does not intersect the boundary of the domain for both the Laplace and the Helmholtz equations. 相似文献
11.
We solve a control problem for the stochastic Burgers equation using the dynamic programming approach. The cost functional
involves exponentially growing functions and the analog of the kinetic energy; the case of a distributed parameter control
is considered. The Hamilton-Jacobi equation is solved by a compactness method and a-priori estimates are obtained thanks to
the regularizing properties of the transition semigroup associated to the stochastic Burgers equation; a fixed point argument
does not seem to apply here.
Entrata in Redazione il 10 dicembre 1998. 相似文献
12.
Akpofure E. Taigbenu 《Numerical Methods for Partial Differential Equations》2010,26(6):1300-1315
This article presents the derivation and implementation of the normal directional flux compatibility equation (relationship) at internal nodes when the Green element formulation that consistently provides accurate estimates of the primary variable, and its normal directional derivative (normal flux) is applied in 2D heterogeneous media to steady and transient potential problems. Such a relationship is required to resolve the closure problem due to having fewer integral equations than the number of unknowns at internal nodes. The derivation of the relationship is based on Stokes' theorem, which transforms the contour integral of the normal directional fluxes into a surface integral that is identically zero. The numerical discretization of the compatibility equation is demonstrated with four numerical examples using the six‐node quadratic triangular and the four and eight‐node rectangular elements. The incorporation of triangular elements into the current formulation demonstrates that the internal compatibility equation can be successfully implemented on irregular grids. The direct calculation of the fluxes significantly enhances the accuracy of the formulation, so that high accuracy, exceeding that of the finite element method, is achieved with very coarse spatial discretization. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
13.
A. S. Golubeva 《Journal of Mathematical Sciences》2000,102(4):4182-4187
An equation of motion of a flat inhomogeheous anisotropic plate is considered. Formal asymptotic solutions are constructed
by applying the space-time ray method. An equation describing the flow of energy is obtained in the form of a continuity equation.
Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 73–82.
Translated by A. S. Golubeva. 相似文献
14.
In this study, we present a conservative local discontinuous Galerkin(LDG) method for numerically solving the two-dimensional nonlinear Schrdinger(NLS) equation. The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux. The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central, alternative and upwind-based flux. We will propose two kinds of time discretization methods for the semi-discrete formulation. One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation. The other one is Krylov implicit integration factor(IIF) method which demands much less computational effort. Various numerical experiments are presented to demonstrate the conservation law of mass and energy, the optimal rates of convergence, and the blow-up phenomenon. 相似文献
15.
S. Arul Veda Manickam Amiya K. Pani Sang K. Chung 《Numerical Methods for Partial Differential Equations》1998,14(6):695-716
A second-order splitting method is applied to a KdV-like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L2 and L∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin–Bona–Mahony) and BBMB (Benjamin–Bona–Mahony–Burgers) equations and the well-known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695–716, 1998 相似文献
16.
The overlapping Schwarz waveform relaxation method is a parallel iterative method for solving time-dependent PDEs. Convergence of the method for the linear heat equation has been studied under infinity norm but it was unknown under the energy norm at the continuous level. The question is interesting for applications concerning fluxes or gradients of the solutions. In this work, we show that the energy norm of the errors of iterates is bounded by their infinity norm. Therefore, we give an affirmative answer to this question for the first time. 相似文献
17.
A boundary value problem for a second-order nonlinear singularly perturbed differential equation is considered for the case
in which there is variation of stability caused by the intersection of roots of the degenerate equation. By the method of
differential inequalities, we prove the existence of a solution such that the limit solution is nonsmooth.
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 354–362, March, 1998.
This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-00694. 相似文献
18.
A sixth-order finite volume method is proposed to solve the Poisson equation for two- and three-dimensional geometries involving Dirichlet condition on curved boundary domains where a new technique is introduced to preserve the sixth-order approximation for non-polygonal or non-polyhedral domains. On the other hand, a specific polynomial reconstruction is used to provide accurate fluxes for elliptic operators even with discontinuous diffusion coefficients. Numerical tests covering a large panel of situations are addressed to assess the performances of the method. 相似文献
19.
An approximation model is proposed for an elliptical equation with complex rapidly varying coefficients. An efficient numerical
method is developed and implemented. A problem of geoelectricity requiring solution of an equation in this setting is investigated.
This research was partially supported by the Russian Foundation for Basic Research (grant No. 96-05-64340) and by the Interuniversity
Scientific Program “Russian Universities: Basic Research.”
Translated from Chislennye Metody v Matematicheskoi Fizike, Moscow State University, pp. 37–45, 1998. 相似文献
20.
Fayssal Benkhaldoun Jaroslav Fořt Khaled Hassouni Jan Karel 《Journal of Computational and Applied Mathematics》2012
The paper deals with the numerical solution of a basic 2D model of the propagation of an ionization wave. The system of equations describing this propagation consists of a coupled set of reaction–diffusion-convection equations and a Poissons equation. The transport equations are solved by a finite volume method on an unstructured triangular adaptive grid. The upwind scheme and the diamond scheme are used for the discretization of the convection and diffusion fluxes, respectively. The Poisson equation is also discretized by the diamond scheme. Numerical results are presented. We deal in more detail with numerical tests of the grid adaptation technique and its influence on the numerical results. An original behavior is observed. The grid refinement is not sufficient to obtain accurate results for this particular phenomenon. Using a second order scheme for convection is necessary. 相似文献