排序方式: 共有57条查询结果,搜索用时 15 毫秒
21.
将非协调元应用于描述细菌传播的反应扩散方程组的初边值问题.借助单元的一些特性和非协调误差估计技巧,分别在半离散和全离散有限元格式下,研究了其数值解与精确解的误差估计,得到了最优的误差估计以及超逼近结果. 相似文献
22.
We derive bilinear forms and Casoratian solutions for two semi-discrete potential Korteweg-de Vries equar tions.Their continuum limits go to the counterparts of the continuous potential Korteweg-de Vries equation. 相似文献
23.
We develop and analyze an adaptive hybridized Interior Penalty
Discontinuous Galerkin (IPDG-H) method for H(curl)-elliptic
boundary value problems in 2D or 3D arising from a
semi-discretization of the eddy currents equations. The method can
be derived from a mixed formulation of the given boundary value
problem and involves a Lagrange multiplier that is an approximation
of the tangential traces of the primal variable on the interfaces of
the underlying triangulation of the computational domain. It is
shown that the IPDG-H technique can be equivalently formulated and
thus implemented as a mortar method. The mesh adaptation is based on
a residual-type a posteriori error estimator consisting of element
and face residuals. Within a unified framework for adaptive finite
element methods, we prove the reliability of the estimator up to a
consistency error. The performance of the adaptive symmetric IPDG-H
method is documented by numerical results for representative test
examples in 2D. 相似文献
24.
Liying Huang David H. Y. Yen 《Numerical Methods for Partial Differential Equations》1997,13(4):331-355
A Gauss–Galerkin finite-difference method is proposed for the numerical solution of a class of linear, singular parabolic partial differential equations in two space dimensions. The method generalizes a Gauss–Galerkin method previously used for treating similar singular parabolic partial differential equations in one space dimension. Two test problems are studied and the numerical results are presented. These numerical results are encouraging and suggest that the proposed method is efficient in treating singular parabolic partial differential equations of the type considered here. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13 : 331–355, 1997 相似文献
25.
We consider a mathematical model which describes the contactbetween a linearly elastic body and an obstacle, the so-calledfoundation. The process is quasistatic and the contact is bilateral,i.e. there is no loss of contact during the process. The frictionis modelled with Tresca's law. The variational formulation ofthe problem is a nonlinear evolutionary inequality for the displacementfield which has a unique solution under certain assumptionson the given data. We study spatially semi-discrete and fullydiscrete schemes for the problem with finite-difference discretizationin time and finite-element discretization in space. The numericalschemes have unique solutions. We show the convergence of thescheme under the basic solution regularity. Under appropriateregularity assumptions on the solution, we derive optimal ordererror estimates. Finally, we present numerical results in thestudy of two-dimensional test problems. 相似文献
26.
本文讨论了广义混合非线性Schrdinger 方程的周期初值问题,构造了守恒的半离散Fourier 拟谱格式,对其近似解进行了先验估计,并证明了格式的收敛性.证明了该方程存在孤立子解,并给出其孤立子解的精确表达式.研究了线性化方程的稳定性问题,即在初值有扰动的情况下,该方程只有振荡解和鞍点.最后,通过数值例子验证了格式的可信性,数值计算表明,本格式时间方向可取大步长且是长时间稳定的,我们还计算了孤立子解,并绘出了在初值有扰动的情况下,相空间的轨线图. 相似文献
27.
在各向异性网格下,针对一类非线性sine-Gordon方程利用最简单的双线性元Q_(11)及Q_(01)×Q_(10)元提出了一个自然满足Brezzi-Babuska条件的最低阶混合元新模式.基于Q_(11)元的积分恒等式结果,建立了插值与Ritz投影之间在H~1模意义下的超收敛估计,再结合关于Q_(01)×Q_(10)元的高精度分析方法和插值后处理技术,对于半离散和全离散格式,均导出了关于原始变量u和流量p=-▽u分别在H~1模和L~2模意义下单独利用插值或Ritz投影所无法得到的超逼近性和超收敛结果.最后,我们对其它一些著名单元也进行了分析,进一步验证了所选单元的合理性和独特优势. 相似文献
28.
29.
This paper considers weak Galerkin finite element approximations on
polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model. The spatial discretization uses piecewise polynomials of degree $k (k ≥ 1)$ for the stress
approximation, degree $k+1$ for the velocity approximation, and degree $k$ for the numerical trace of velocity on the inter-element boundaries. The temporal discretization in the fully discrete method adopts a backward Euler difference scheme. We
show the existence and uniqueness of the semi-discrete and fully discrete solutions,
and derive optimal a priori error estimates. Numerical examples are provided to
support the theoretical analysis. 相似文献
30.
We introduce a new high-resolution central scheme for multidimensional Hamilton–Jacobi equations. The scheme retains the simplicity of the non-oscillatory central schemes developed by C.-T. Lin and E. Tadmor (in press, SIAM J. Sci. Comput.), yet it enjoys a smaller amount of numerical viscosity, independent of 1/Δt. By letting Δt↓0 we obtain a new second-order central scheme in the particularly simple semi-discrete form, along the lines of the new semi-discrete central schemes recently introduced by the authors in the context of hyperbolic conservation laws. Fully discrete versions are obtained with appropriate Runge–Kutta solvers. The smaller amount of dissipation enables efficient integration of convection-diffusion equations, where the accumulated error is independent of a small time step dictated by the CFL limitation. The scheme is non-oscillatory thanks to the use of nonlinear limiters. Here we advocate the use of such limiters on second discrete derivatives, which is shown to yield an improved high resolution when compared to the usual limitation of first derivatives. Numerical experiments demonstrate the remarkable resolution obtained by the proposed new central scheme. 相似文献