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1.
Michal Křížek Jan Němec Tomáš Vejchodský 《Advances in Computational Mathematics》2001,15(1-4):219-236
We propose and examine the primal and dual finite element method for solving an axially symmetric elliptic problem with mixed boundary conditions. We derive an a posteriori error estimate and generalize the method used for a nonlinear elliptic problem. Finally, an a posteriori error estimate for a nonlinear parabolic problem based on the concept of hierarchical finite element basis functions is introduced. 相似文献
2.
Olaf Steinbach 《Numerische Mathematik》2002,90(4):775-786
Summary. In this paper we investigate a stability estimate needed in hybrid finite and boundary element methods, especially in hybrid
coupled domain decomposition methods including mortar finite elements. This stability estimate is equivalent to the stability
of a generalized projection in certain Sobolev spaces. Using piecewise linear trial spaces and appropriate piecewise constant test spaces,
the stability of the generalized projection is proved assuming some mesh conditions locally.
Received April 11, 2000 / Revised version received February 15, 2001 / Published online July 25, 2001 相似文献
3.
We consider the a posteriori error estimates for finite element approximations of the Stokes–Darcy system. The finite element spaces adopted are the Hood–Taylor element for the velocity and the pressure in fluid region and conforming piecewise quadratic element for the pressure in porous media region. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
4.
Rodolfo Araya Gabriel R. Barrenechea Abner Poza 《Journal of Computational and Applied Mathematics》2008
In this work we present an adaptive strategy (based on an a posteriori error estimator) for a stabilized finite element method for the Stokes problem, with and without a reaction term. The hierarchical type estimator is based on the solution of local problems posed on appropriate finite dimensional spaces of bubble-like functions. An equivalence result between the norm of the finite element error and the estimator is given, where the dependence of the constants on the physics of the problem is explicited. Several numerical results confirming both the theoretical results and the good performance of the estimator are given. 相似文献
5.
Chun-jiaBi Li-kangLi 《计算数学(英文版)》2004,22(3):475-488
In this paper, we construct and analyse a mortar finite volume method for the discretization for the biharmonic problem in R2. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order H2-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established. 相似文献
6.
Joachim Gwinner 《Applicable analysis》2013,92(1-4):179-192
Céa's approximation lemma is extended to variational inequalities which are defined by strongly monotone operators in closed convex subsets of linear normed spaces. This abstract error estimate is applied to the finite element discretization of a nonlinear elliptic two-sided obstacle problem providing an asymptotic error estimate for a smooth enough solution. 相似文献
7.
The Zienkiewicz–Zhu error estimate is slightly modified for the hierarchical p-refinement, and is then applied to three plane elastostatic problems to demonstrate its effectiveness. In each case, the error decreases rapidly with an increase in the number of degrees of freedom. Thus Zienkiewicz–Zhu's error estimate can be used in the hp-refinement of finite element meshes. 相似文献
8.
1. IntroductionThere are many work to investigate the stability of the mired finite element methodfor the saddle-point problems, i.e., to construct the finite element spaces, such that theso-called discrete BB-codition is satisfied (c.f. [1],[21,[7],[81 and the references therein).To circumvent the discrete BB-conditon, recently there has been an increased interest inuse of least-squares approach for the solution of the mixed finite element approximationof the saddel-point problem (c.f.[3]--[… 相似文献
9.
HUANG Jianguo SHI Zhongci & XU Yifeng Department of Mathematics Shanghai Jiao long University Shanghai China Division of Computational Science E-lnstitute of Shanghai Universities Shanghai Normal University Shanghai China Institute of Computational Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics Chinese University of Hong Kong Shatin N. T. Hong Kong China 《中国科学A辑(英文版)》2006,49(1):109-129
A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method. 相似文献
10.
This paper introduces a kind of multigrid finite element method for the coupled semilinear elliptic equations. Instead of the common way of directly solving the coupled semilinear elliptic problems on some fine spaces, the presented method transforms the solution of the coupled semilinear elliptic problem into a series of solutions of the corresponding decoupled linear boundary value problems on the sequence of multilevel finite element spaces and some coupled semilinear elliptic problems on a very low dimensional space. The decoupled linearized boundary value problems can be solved by some multigrid iterations efficiently. The optimal error estimate and optimal computational work are proved theoretically and demonstrated numerically. Moreover, the requirement of bounded second‐order derivatives of the nonlinear term in the existing multigrid method is reduced to a Lipschitz continuous condition in the proposed method. 相似文献
11.
该文将一个低阶Crouzeix-Raviart型非协调三角形元应用到非定常Navier-Stokes方程,给出了其质量集中有限元逼近格式.在不需要传统Ritz-Volterra投影下,通过引入两个辅助有限元空间对边界进行估计的技巧,在各向异性网格下导出了速度的L~2模和能量模及压力的L~2模的误差估计. 相似文献
12.
Matteo Negri 《Numerical Functional Analysis & Optimization》2013,34(9-10):957-982
We compute explicitly the anisotropy effect in the H 1 term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations. 相似文献
13.
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
14.
We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger-Reissner mixed formulation of the elasticty equations, when standard discontinuous finite element spaces are used to approximate the displacement field. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and there is one for each positive value of the polynomial degree used for the displacements. For each degree, these provide a stable finite element discretization. The construction of the spaces is closely tied to discretizations of the elasticity complex and can be viewed as the three-dimensional analogue of the triangular element family for plane elasticity previously proposed by Arnold and Winther.
15.
Summary. There have been many efforts, dating back four decades, to develop stable mixed finite elements for the stress-displacement
formulation of the plane elasticity system. This requires the development of a compatible pair of finite element spaces, one
to discretize the space of symmetric tensors in which the stress field is sought, and one to discretize the space of vector
fields in which the displacement is sought. Although there are number of well-known mixed finite element pairs known for the
analogous problem involving vector fields and scalar fields, the symmetry of the stress field is a substantial additional
difficulty, and the elements presented here are the first ones using polynomial shape functions which are known to be stable.
We present a family of such pairs of finite element spaces, one for each polynomial degree, beginning with degree two for
the stress and degree one for the displacement, and show stability and optimal order approximation. We also analyze some obstructions
to the construction of such finite element spaces, which account for the paucity of elements available.
Received January 10, 2001 / Published online November 15, 2001 相似文献
16.
The effects of orientation and shape of filler particles on the elastic properties of composites have been analyzed. The elastic
constants of a composite with irregularly oriented filler particles were calculated by using the method of orientational averaging
of the properties of a representative structural element. The elastic constants of the structural element were found according
to a known generalized Eshelby solution for a finite concentration of ellipsoidal inclusions. The diagrams of elasticity anisotropy
for a transversely isotropic structural element and an orthotropic composite with irregularly oriented inclusions are presented.
A quantitative estimate for the degree of anisotropy of elastic properties of composites is suggested. Data on the influence
of shape anisometry of inclusions on the anisotropy coefficient of filled composites are also reported. 相似文献
17.
Rob Stevenson 《Numerische Mathematik》1997,78(2):269-303
Summary. In this paper, we introduce a multi-level direct sum space decomposition of general, possibly locally refined linear or multi-linear
finite element spaces. The resulting additive Schwarz preconditioner is optimal for symmetric second order elliptic problems.
Moreover, it turns out to be robust with respect to coefficient jumps over edges in the coarsest mesh, perturbations with
positive zeroth order terms, and, after a further decomposition of the spaces, also with respect to anisotropy along the grid
lines. Important for an efficient implementation is that stable bases of the subspaces defining our decomposition, consisting
of functions having small supports can be easily constructed.
Received September 8, 1995 / Revised version received October 31, 1996 相似文献
18.
孙同军 《高等学校计算数学学报(英文版)》2001,10(1)
1 IntroductionADI Galerkin methods were first formulated for the solution of nonlinear parabolic andlinear second-order hyperbolic problems on rectangular regions by Douglas and Dupont[1 ] .These methods combine alternating-direction method and Galerkin finite element methodtogether.So,they have the advantage of reducing the solution of a multidimensional problemto the solution of sets of independent one-dimensional problems,decreasing the amount ofcalculation,natural parallelism and highe… 相似文献
19.
Madhusmita Tripathy 《Numerical Functional Analysis & Optimization》2013,34(3):320-337
We derive superconvergence result for H 1-Galerkin mixed finite element method for second-order elliptic equations over rectangular partitions. Compared to standard mixed finite element procedure, the method is not subject to the Ladyzhenskaya–Bab?ska–Brezzi (LBB) condition and the approximating finite element spaces are allowed to be of different polynomial degrees. Superconvergence estimate of order 𝒪(h k+3), where k ≥ 1 is the order of the approximating polynomials employed in the Raviart–Thomas elements, is established for the flux via a postprocessing technique. 相似文献
20.
Gabriel N. Gatica Norbert Heuer Ernst P. Stephan 《Mathematical Methods in the Applied Sciences》2001,24(3):179-191
We consider the coupling of dual‐mixed finite elements and boundary elements to solve a mixed Dirichlet–Neumann problem of plane elasticity. We derive an a‐posteriori error estimate that is based on the solution of local Dirichlet problems and on a residual term defined on the coupling interface. The general error estimate does not make use of any special finite element or boundary element spaces. Here the residual term is given in a negative order Sobolev norm. In practical applications, where a certain boundary element subspace is used, this norm can be estimated by weighted local L2‐norms. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献