共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we derive an a posteriori error bound for the Lagrange-Galerkin discretisation of an unsteady (linear) convection-diffusion problem, assuming only that the underlying space-time mesh is nondegenerate. The proof of this error bound is based on strong stability estimates of an associated dual problem, together with the Galerkin orthogonality of the finite element method. Based on this a posteriori bound, we design and implement the corresponding adaptive algorithm to ensure global control of the error with respect to a user-defined tolerance.
2.
Summary. In this paper, we study a multiscale finite element method for solving a class of elliptic problems with finite number of
well separated scales. The method is designed to efficiently capture the large scale behavior of the solution without resolving
all small scale features. This is accomplished by constructing the multiscale finite element base functions that are adaptive
to the local property of the differential operator. The construction of the base functions is fully decoupled from element
to element; thus the method is perfectly parallel and is naturally adapted to massively parallel computers. We present the
convergence analysis of the method along with the results of our numerical experiments. Some generalizations of the multiscale
finite element method are also discussed.
Received April 17, 1998 / Revised version received March 25, 2000 / Published online June 7, 2001 相似文献
3.
Summary Recently, Hughes et al. [11, 12] proposed new finite element schemes of Petrov-Galerkin type for solving the Stokes problem which do not require the discrete version of the Ladyshenskaya-Babuka-Brezzi-condition (LBB-condition). In this paper we derive a conforming finite element method for solving the stationary Navier-Stokes equations which combines the advantages of arbitrary finite element spaces for velocity/pressure with the favourable properties of the streamline diffusion method in the case of moderate and high Reynolds number. 相似文献
4.
Zhiqiang Cai 《Numerische Mathematik》1990,58(1):713-735
Summary The finite volume element method (FVE) is a discretization technique for partial differential equations. It uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations, then restricts the admissible functions to a finite element space to discretize the solution. this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with FVE based on triangulations with linear finite element spaces and a general type of control volume. We establishO(h) estimates of the error in a discreteH
1 semi-norm. Under an additional assumption of local uniformity of the triangulation the estimate is improved toO(h
2). Results on the effects of numerical integration are also included.This research was sponsored in part by the Air Force Office of Scientific Research under grant number AFOSR-86-0126 and the National Science Foundation under grant number DMS-8704169. This work was performed while the author was at the University of Colorado at Denver 相似文献
5.
Summary. In this paper, we develop and analyze a new finite element method called the sparse finite element method for second order
elliptic problems. This method involves much fewer degrees of freedom than the standard finite element method. We show nevertheless
that such a sparse finite element method still possesses the superconvergence and other high accuracy properties same as those
of the standard finite element method. The main technique in our analysis is the use of some integral identities.
Received October 1, 1995 / Revised version received August 23, 1999 / Published online February 5, 2001 相似文献
6.
Carsten Carstensen 《Numerische Mathematik》1999,82(4):577-597
Summary. The finite element method is a reasonable and frequently utilised tool for the spatial discretization within one time-step
in an elastoplastic evolution problem. In this paper, we analyse the finite element discretization and prove a priori and
a posteriori error estimates for variational inequalities corresponding to the primal formulation of (Hencky) plasticity.
The finite element method of lowest order consists in minimising a convex function on a subspace of continuous piecewise linear
resp. piecewise constant trial functions. An a priori error estimate is established for the fully-discrete method which shows
linear convergence as the mesh-size tends to zero, provided the exact displacement field u is smooth. Near the boundary of the plastic domain, which is unknown a priori, it is most likely that u is non-smooth. In this situation, automatic mesh-refinement strategies are believed to improve the quality of the finite
element approximation. We suggest such an adaptive algorithm on the basis of a computable a posteriori error estimate. This
estimate is reliable and efficient in the sense that the quotient of the error by the estimate and its inverse are bounded
from above. The constants depend on the hardening involved and become larger for decreasing hardening.
Received May 7, 1997 / Revised version received August 31, 1998 相似文献
7.
On the solution a of second order singularly-perturbed boundary value problem by the Sinc-Galerkin method 总被引:1,自引:0,他引:1
Mohamed El-Gamel John R. Cannon 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(1):45-58
Sinc methods are now recognized as an efficient numerical method for problems whose solutions may have singularities, or infinite domains, or boundary layers. This work deals with the Sinc-Galerkin method for solving second order singularly perturbed boundary value problems. The method is then tested on linear and nonlinear examples and a comparison with spline method and finite element scheme is made. It is shown that the Sinc-Galerkin method yields better results.Received: January 3, 2003; revised: July 14, 2003 相似文献
8.
Summary.
An explicit finite element method for numerically solving
the drift-diffusion semiconductor device equations in two space dimensions
is analyzed.
The method is based on the use of a mixed finite element method for the approximation
of the electric field and a discontinuous
upwinding finite element method for the approximation
of the electron and hole concentrations. The mixed method gives an approximate electric
field in the precise form needed by the discontinuous method, which is trivially
conservative and fully parallelizable. It is proven that the method produces
uniformly bounded concentrations and electric fields and that it converges
to the exact solution provided there is a convergent subsequence of the electron
concentrations. Numerical simulations are presented that display the
performance of the method and indicate the behavior of the solution.
Received
September 9, 1993 / Revised version received May 25,
1994 相似文献
9.
The discretization by finite elements of a model variational problem for a clamped loaded beam is studied with emphasis on the effect of the beam thickness, which appears as a parameter in the problem, on the accuracy. It is shown that the approximation achieved by a standard finite element method degenerates for thin beams. In contrast a large family of mixed finite element methods are shown to yield quasioptimal approximation independent of the thickness parameter. The most useful of these methods may be realized by replacing the integrals appearing in the stiffness matrix of the standard method by Gauss quadratures. 相似文献
10.
In this article, we present a new fully discrete finite element nonlinear Galerkin method, which are well suited to the long
time integration of the Navier-Stokes equations. Spatial discretization is based on two-grid finite element technique; time
discretization is based on Euler explicit scheme with variable time step size. Moreover, we analyse the boundedness, convergence
and stability condition of the finite element nonlinear Galerkin method. Our discussion shows that the time step constraints
of the method depend only on the coarse grid parameter and the time step constraints of the finite element Galerkin method depend on the fine grid parameter under the same convergence accuracy.
Received February 2, 1994 / Revised version received December 6, 1996 相似文献
11.
Alexander Eydeland 《Numerische Mathematik》1984,43(1):59-82
Summary A general globally convergent iterative method for solving nonlinear variational problems is introduced. The method is applied to a temperature control problem and to the minimal surface problem. Several aspects of finite element implementation of the method are discussed. 相似文献
12.
Summary The mixed finite element method for the linear elasticity problem is considered. We propose a systematic way of designing methods with optimal convergence rates for both the stress tensor and the displacement. The ideas are applied in some examples. 相似文献
13.
Carmen Dietel 《Numerische Mathematik》1987,51(4):415-428
Summary The paper deals with some finite element approximation of stationary heat conduction problems on regions which can be partitioned into rectangular subregions. By a special superelement-technique employing fast elimination of the inner nodal parameters, the original finite element problem is reduced to a smaller problem, which is only connected with the nodes on the boundary of the superelements. To solve the reduced system of finite element equations, an efficient iterative algorithm is proposed. This algorithm is based either on the conjugate gradient method or the Tshebysheff method, using a special matrix by vector multiplication procedure. The explicit form of the matrix is not used. The presented numerical method is asymptotically optimal with respect to the memory requirement as well as to the operation count. 相似文献
14.
Summary In this paper we describe a nonconforming finite element method to compute the MHD spectrum of a plasma in a toroïdal configuration. We show that this method leads to a good approximation of the spectrum. 相似文献
15.
Noboru Kikuchi 《Numerische Mathematik》1981,37(1):105-120
Summary This study establishes an error estimate for a penalty-finite element approximation of the variational inequality obtained by a class of obstacle problems. By special identification of the penalty term, we first show that the penalty solution converges to the solution of a mixed formulation of the variational inequality. The rate of convergence of the penalization is where is the penalty parameter. To obtain the error of finite element approximation, we apply the results obtained by Brezzi, Hager and Raviart for the mixed finite element method to the variational inequality. 相似文献
16.
Likang Li 《Numerische Mathematik》1990,57(1):413-420
Summary In this paper the discretization of the Timoshenko Beam problem by thep and theh-p versions of the finite element method is considered. Optimal error estimates are established. The locking phenomenon disappears as the thickness of the beam decreases. 相似文献
17.
Least-squares mixed finite element methods
for non-selfadjoint elliptic problems: I. Error estimates
Summary.
A least-squares mixed finite element
method for general second-order non-selfadjoint
elliptic problems in two- and three-dimensional domains
is formulated and analyzed. The finite element spaces for
the primary solution approximation
and the flux approximation
consist of piecewise polynomials of degree
and respectively.
The method is mildly nonconforming on the boundary.
The cases and
are studied.
It is proved that the method is not subject to the LBB-condition.
Optimal - and
-error estimates are derived for
regular finite element partitions.
Numerical experiments, confirming the theoretical rates of
convergence, are presented.
Received
October 15, 1993 / Revised version received August 2, 1994 相似文献
18.
This paper provides an analysis of a fractional-step projection method to compute incompressible viscous flows by means of
finite element approximations. The analysis is based on the idea that the appropriate functional setting for projection methods
must accommodate two different spaces for representing the velocity fields calculated respectively in the viscous and the
incompressible half steps of the method. Such a theoretical distinction leads to a finite element projection method with a
Poisson equation for the incremental pressure unknown and to a very practical implementation of the method with only the intermediate
velocity appearing in the numerical algorithm. Error estimates in finite time are given. An extension of the method to a problem
with unconventional boundary conditions is also considered to illustrate the flexibility of the proposed method.
Received October 2, 1995 / Revised version received July 9, 1997 相似文献
19.
Summary In theh-version of the finite element method, convergence is achieved by refining the mesh while keeping the degree of the elements fixed. On the other hand, thep-version keeps the mesh fixed and increases the degree of the elements. In this paper, we prove estimates showing the simultaneous dependence of the order of approximation on both the element degrees and the mesh. In addition, it is shown that a proper design of the mesh and distribution of element degrees lead to a better than polynomial rate of convergence with respect to the number of degrees of freedom, even in the presence of corner singularities. Numerical results comparing theh-version,p-version, and combinedh-p-version for a one dimensional problem are presented. 相似文献
20.
Nonlinear Galerkin methods and mixed finite elements:
two-grid algorithms for the Navier-Stokes equations 总被引:14,自引:0,他引:14
Summary.
A nonlinear Galerkin method using mixed finite
elements is presented for the two-dimensional
incompressible Navier-Stokes equations. The
scheme is based on two finite element spaces
and for the approximation of the velocity,
defined respectively on one coarse grid with grid
size and one fine grid with grid size and
one finite element space for the approximation
of the pressure. Nonlinearity and time
dependence are both treated on the coarse space.
We prove that the difference between the new
nonlinear Galerkin method and the standard
Galerkin solution is of the order of $H^2$, both in
velocity ( and pressure norm).
We also discuss a penalized version of our algorithm
which enjoys similar properties.
Received October 5, 1993 / Revised version received November
29, 1993 相似文献