共查询到20条相似文献,搜索用时 31 毫秒
1.
Youngmok Jeon 《Journal of Computational and Applied Mathematics》2010,234(8):2469-2482
We introduce two kinds of the cell boundary element (CBE) methods for convection dominated convection-diffusion equations: one is the CBE method with the exact bubble function and the other with inexact bubble functions. The main focus of this paper is on inexact bubble CBE methods. For inexact bubble CBE methods we introduce a family of numerical methods depending on two parameters, one for control of interior layers and the other for outflow boundary layers. Stability and convergence analysis are provided and numerical tests for inexact bubble CBEs with various choices of parameters are presented. 相似文献
2.
A. Aimi M. DiligentiC. Guardasoni 《Journal of Computational and Applied Mathematics》2011,235(7):1746-1754
We consider two-dimensional interior wave propagation problems with vanishing initial and mixed boundary conditions, reformulated as a system of two boundary integral equations with retarded potential. These latter are then set in a weak form, based on a natural energy identity satisfied by the solution of the differential problem, and discretized by the related energetic Galerkin boundary element method. Numerical results are presented and discussed. 相似文献
3.
A boundary multiplier/fictitious domain method for the steady incompressible Navier-Stokes equations
Summary. We analyze the error of a fictitious-domain method with boundary Lagrange multiplier. It is applied to solve a non-homogeneous
steady incompressible Navier-Stokes problem in a domain with a multiply-connected boundary. The interior mesh in the fictitious
domain and the boundary mesh are independent, up to a mesh-length ratio.
Received February 24, 1999 / Revised version received January 30, 2000 / Published online October 16, 2000 相似文献
4.
C. De Luigi 《Journal of Computational and Applied Mathematics》2010,234(1):181-191
We describe how to use new reduced size polynomial approximations for the numerical solution of the Poisson equation over hypercubes. Our method is based on a non-standard Galerkin method which allows test functions which do not verify the boundary conditions. Numerical examples are given in dimensions up to 8 on solutions with different smoothness using the same approximation basis for both situations. A special attention is paid on conditioning problems. 相似文献
5.
Summary In this paper the convergence analysis of a direct boundary elecment method for the mixed boundary value problem for Laplace equation in a smooth plane domain is given. The method under consideration is based on the collocation solution by constant elements of the corresponding system of boundary integral equations. We prove the convergence of this method, provide asymptotic error estimates for the BEM-solution and give some numerical examples. 相似文献
6.
E. F. Kaasschieter 《BIT Numerical Mathematics》1989,29(4):824-849
Discretizing a symmetric elliptic boundary value problem by a finite element method results in a system of linear equations with a symmetric positive definite coefficient matrix. This system can be solved iteratively by a preconditioned conjugate gradient method. In this paper a preconditioning matrix is proposed that can be constructed for all finite element methods if a mild condition for the node numbering is fulfilled. Such a numbering can be constructed using a variant of the reverse Cuthill-McKee algorithm. 相似文献
7.
Bosco García-Archilla 《Numerische Mathematik》1992,61(1):291-310
Summary A finite-difference method for the integration of the Korteweg-de Vries equation on irregular grids is analyzed. Under periodic boundary conditions, the method is shown to be supraconvergent in the sense that, though being inconsistent, it is second order convergent. However, such a convergence only takes place on grids with an odd number of points per period. When a grid with an even number of points is used, the inconsistency of the method leads to divergence. Numerical results backing the analysis are presented. 相似文献
8.
Summary.
We discuss the effect of cubature errors
when using the Galerkin method for
approximating the solution of Fredholm integral equations in three
dimensions. The accuracy of the cubature method
has to be chosen such that
the error resulting from this further discretization
does not increase the
asymptotic discretization error. We will show that the
asymptotic accuracy
is not influenced provided that polynomials of a certain degree are
integrated exactly by the cubature method. This is done by applying the
Bramble-Hilbert Lemma to the boundary element method.
Received May 24, 1995 相似文献
9.
J. RashidiniaM. Ghasemi 《Journal of Computational and Applied Mathematics》2011,235(8):2325-2342
A numerical method based on B-spline is developed to solve the general nonlinear two-point boundary value problems up to order 6. The standard formulation of sextic spline for the solution of boundary value problems leads to non-optimal approximations. In order to derive higher orders of accuracy, high order perturbations of the problem are generated and applied to construct the numerical algorithm. The error analysis and convergence properties of the method are studied via Green’s function approach. O(h6) global error estimates are obtained for numerical solution of these classes of problems. Numerical results are given to illustrate the efficiency of the proposed method. Results of numerical experiments verify the theoretical behavior of the orders of convergence. 相似文献
10.
On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation 总被引:1,自引:0,他引:1
Summary We describe a quadrature method for the numerical solution of the logarithmic integral equation of the first kind arising from the single-layer approach to the Dirichlet problem for the two-dimensional Helmholtz equation in smooth domains. We develop an error analysis in a Sobolev space setting and prove fast convergence rates for smooth boundary data. 相似文献
11.
In this paper, we consider the div-curl problem posed on nonconvex polyhedral domains. We propose a least-squares method based
on discontinuous elements with normal and tangential continuity across interior faces, as well as boundary conditions, weakly
enforced through a properly designed least-squares functional. Discontinuous elements make it possible to take advantage of
regularity of given data (divergence and curl of the solution) and obtain convergence also on nonconvex domains. In general,
this is not possible in the least-squares method with standard continuous elements. We show that our method is stable, derive
a priori error estimates, and present numerical examples illustrating the method. 相似文献
12.
An interpolation matched interface and boundary (IMIB) method with second-order accuracy is developed for elliptic interface problems on Cartesian grids, based on original MIB method proposed by Zhou et al. [Y. Zhou, G. Wei, On the fictious-domain and interpolation formulations of the matched interface and boundary method, J. Comput. Phys. 219 (2006) 228-246]. Explicit and symmetric finite difference formulas at irregular grid points are derived by virtue of the level set function. The difference scheme using IMIB method is shown to satisfy the discrete maximum principle for a certain class of problems. Rigorous error analyses are given for the IMIB method applied to one-dimensional (1D) problems with piecewise constant coefficients and two-dimensional (2D) problems with singular sources. Comparison functions are constructed to obtain a sharp error bound for 1D approximate solutions. Furthermore, we compare the ghost fluid method (GFM), immersed interface method (IIM), MIB and IMIB methods for 1D problems. Finally, numerical examples are provided to show the efficiency and robustness of the proposed method. 相似文献
13.
Summary In this paper we apply the coupling of boundary integral and finite element methods to solve a nonlinear exterior Dirichlet problem in the plane. Specifically, the boundary value problem consists of a nonlinear second order elliptic equation in divergence form in a bounded inner region, and the Laplace equation in the corresponding unbounded exterior region, in addition to appropriate boundary and transmission conditions. The main feature of the coupling method utilized here consists in the reduction of the nonlinear exterior boundary value problem to an equivalent monotone operator equation. We provide sufficient conditions for the coefficients of the nonlinear elliptic equation from which existence, uniqueness and approximation results are established. Then, we consider the case where the corresponding operator is strongly monotone and Lipschitz-continuous, and derive asymptotic error estimates for a boundary-finite element solution. We prove the unique solvability of the discrete operator equations, and based on a Strang type abstract error estimate, we show the strong convergence of the approximated solutions. Moreover, under additional regularity assumptions on the solution of the continous operator equation, the asymptotic rate of convergenceO (h) is obtained.The first author's research was partly supported by the U.S. Army Research Office through the Mathematical Science Institute of Cornell University, by the Universidad de Concepción through the Facultad de Ciencias, Dirección de Investigación and Vicerretoria, and by FONDECYT-Chile through Project 91-386. 相似文献
14.
An efficient multigrid-FEM method for the detailed simulation of solid–liquid two phase flows with large number of moving particles is presented. An explicit fictitious boundary method based on a FEM background grid which covers the whole computational domain and can be chosen independently from the particles of arbitrary shape, size and number is used to deal with the interactions between the fluid and the particles. Since the presented method treats the fluid part, the calculation of forces and the movement of particles in a subsequent manner, it is potentially powerful to efficiently simulate real particulate flows with huge number of particles. The presented method is first validated using a series of simple test cases, and then as an illustration, simulations of three big disks plunging into 2000 small particles, and of sedimentation of 10,000 particles in a cavity are presented. 相似文献
15.
The boundary node method (BNM) exploits the dimensionality of the boundary integral equation (BIE) and the meshless attribute of the moving least-square (MLS) approximations. However, since MLS shape functions lack the property of a delta function, it is difficult to exactly satisfy boundary conditions in BNM. Besides, the system matrices of BNM are non-symmetric. 相似文献
16.
Runge-Kutta methods without order reduction for linear initial boundary value problems 总被引:1,自引:0,他引:1
Isaías Alonso-Mallo 《Numerische Mathematik》2002,91(4):577-603
Summary. It is well-known the loss of accuracy when a Runge–Kutta method is used together with the method of lines for the full discretization
of an initial boundary value problem. We show that this phenomenon, called order reduction, is caused by wrong boundary values
in intermediate stages. With a right choice, the order reduction can be avoided and the optimal order of convergence in time
is achieved. We prove this fact for time discretizations of abstract initial boundary value problems based on implicit Runge–Kutta
methods. Moreover, we apply these results to the full discretization of parabolic problems by means of Galerkin finite element
techniques. We present some numerical examples in order to confirm that the optimal order is actually achieved.
Received July 10, 2000 / Revised version received March 13, 2001 / Published online October 17, 2001 相似文献
17.
Ezequiel Dratman 《Journal of Computational and Applied Mathematics》2010,233(9):2339-2350
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the “continuous” equation. Furthermore, we exhibit an algorithm computing an ε-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required. 相似文献
18.
M.A. El-Gebeily K.M. Furati Donal O’Regan Ravi Agarwal 《Journal of Computational and Applied Mathematics》2009
We investigate the approximation of the solutions of a class of nonlinear second order singular boundary value problems with a self-adjoint linear part. Our strategy involves two ingredients. First, we take advantage of certain boundary condition functions to obtain well behaved functions of the solutions. Second, we integrate the problem over an interval that avoids the singularity. We are able to prove a uniform convergence result for the approximate solutions. We describe how the approximation is constructed for the various values of the deficiency index associated with the differential equation. The solution of the nonlinear problem is obtained by a globally convergent iterative method. 相似文献
19.
Summary. We study some additive Schwarz algorithms for the version Galerkin boundary element method applied to some weakly singular and hypersingular integral equations of the first
kind. Both non-overlapping and overlapping methods are considered. We prove that the condition numbers of the additive Schwarz
operators grow at most as independently of h, where p is the degree of the polynomials used in the Galerkin boundary element schemes and h is the mesh size. Thus we show that additive Schwarz methods, which were originally designed for finite element discretisation
of differential equations, are also efficient preconditioners for some boundary integral operators, which are non-local operators.
Received June 15, 1997 / Revised version received July 7, 1998 / Published online February 17, 2000 相似文献
20.
Summary. A Galerkin approximation of both strongly and hypersingular boundary integral equation (BIE) is considered for the solution
of a mixed boundary value problem in 3D elasticity leading to a symmetric system of linear equations. The evaluation of Cauchy
principal values (v. p.) and finite parts (p. f.) of double integrals is one of the most difficult parts within the implementation
of such boundary element methods (BEMs). A new integration method, which is strictly derived for the cases of coincident elements
as well as edge-adjacent and vertex-adjacent elements, leads to explicitly given regular integrand functions which can be
integrated by the standard Gauss-Legendre and Gauss-Jacobi quadrature rules. Problems of a wide range of integral kernels
on curved surfaces can be treated by this integration method. We give estimates of the quadrature errors of the singular four-dimensional
integrals.
Received June 25, 1995 / Revised version received January 29, 1996 相似文献