共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we analyze the finite element discretization for the first-order system least squares mixed model for the second-order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress, respectively. Moreover, on arbitrary regular quadrilaterals, we propose new variants of both the rotated nonconforming element and the lowest-order Raviart-Thomas element.
2.
Jan H. Brandts 《Applications of Mathematics》2009,54(3):225-235
We show that a non-standard mixed finite element method proposed by Barrios and Gatica in 2007, is a higher order perturbation
of the least-squares mixed finite element method. Therefore, it is also superconvergent whenever the least-squares mixed finite
element method is superconvergent. Superconvergence of the latter was earlier investigated by Brandts, Chen and Yang between
2004 and 2006. Since the new method leads to a non-symmetric system matrix, its application seems however more expensive than
applying the least-squares mixed finite element method.
Dedicated to Ivan Hlaváček on the occasion of his 75th birthday 相似文献
3.
Natural superconvergence of the least-squares finite element method is surveyed for the one-and two-dimensional Poisson equation.
For two-dimensional problems, both the families of Lagrange elements and Raviart-Thomas elements have been considered on uniform
triangular and rectangular meshes. Numerical experiments reveal that many superconvergence properties of the standard Galerkin
method are preserved by the least-squares finite element method.
The second author was supported in part by the US National Science Foundation under Grant DMS-0612908. 相似文献
4.
Schoberl Joachim; Melenk Jens M.; Pechstein Clemens; Zaglmayr Sabine 《IMA Journal of Numerical Analysis》2008,28(1):1-24
5.
Shangyou Zhang. 《Mathematics of Computation》2005,74(250):543-554
A natural mixed-element approach for the Stokes equations in the velocity-pressure formulation would approximate the velocity by continuous piecewise-polynomials and would approximate the pressure by discontinuous piecewise-polynomials of one degree lower. However, many such elements are unstable in 2D and 3D. This paper is devoted to proving that the mixed finite elements of this - type when satisfy the stability condition--the Babuska-Brezzi inequality on macro-tetrahedra meshes where each big tetrahedron is subdivided into four subtetrahedra. This type of mesh simplifies the implementation since it has no restrictions on the initial mesh. The new element also suits the multigrid method.
6.
7.
Jan H. Brandts 《Applications of Mathematics》1999,44(6):407-419
We will investigate the possibility to use superconvergence results for the mixed finite element discretizations of some time-dependent partial differential equations in the construction of a posteriori error estimators. Since essentially the same approach can be followed in two space dimensions, we will, for simplicity, consider a model problem in one space dimension. 相似文献
8.
This article considers a mixed finite element method for linear elasticity. It is based on a modified mixed formulation that enforces the continuity of the stress weakly by adding a jump term of the approximated stress on interior edges. The symmetric stress are approximated by nonconforming linear elements and the displacement by piecewise constants. We establish ??(h) error bound in the (broken) L2 norm for the divergence of the stress and ??(h) error bound in the L2 norm for both the displacement and the stress tensor. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005. 相似文献
9.
Two new least-squares mixed finite element procedures are formulated for solving convection-dominated Sobolev equations. Optimal
H(div;Ω)×H
1(Ω) norms error estimates are derived under the standard mixed finite spaces. Moreover, these two schemes provide the approximate
solutions with first-order and second-order accuracy in time increment, respectively. 相似文献
10.
Hui Guo 《Applied mathematics and computation》2011,217(9):4682-4690
In this paper, we introduce two novel split least-squares mixed element procedures for pseudo-parabolic equations. By selecting the least-squares functional properly, each procedure can be split into two independent symmetric positive definite sub-procedures. One of sub-procedures is for the primitive unknown variable u, which is the same as the standard Galerkin finite element procedure and the other is for the introduced flux variable σ. Optimal order error estimates are developed. A numerical example is given to show the efficiency of the introduced schemes. 相似文献
11.
This paper introduces a new family of nonconforming mixed finite elements for solving the linear elasticity equations on simplicial grids. Besides, this paper describes the construction of the lowest order basis functions. The construction only involves simple computations due to the new explicit stress shape function spaces and the procedure applies for high order cases. Numerical experiments for four benchmark problems in mechanics indicate the robust locking‐free behavior and show that the lowest order nonconforming mixed method leads to smaller stress errors than the first and second order standard Galerkin methods for the nearly incompressible case. 相似文献
12.
Suh-Yuh Yang Ching L. Chang 《Numerical Methods for Partial Differential Equations》1998,14(3):297-315
A new stress-pressure-displacement formulation for the planar elasticity equations is proposed by introducing the auxiliary variables, stresses, and pressure. The resulting first-order system involves a nonnegative parameter that measures the material compressibility for the elastic body. A two-stage least-squares finite element procedure is introduced for approximating the solution to this system with appropriate boundary conditions. It is shown that the two-stage least-squares scheme is stable and, with respect to the order of approximation for smooth exact solutions, the rates of convergence of the approximations for all the unknowns are optimal both in the H1-norm and in the L2-norm. Numerical experiments with various values of the parameter are examined, which demonstrate the theoretical estimates. Among other things, computational results indicate that the behavior of convergence is uniform in the nonnegative parameter. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 297–315, 1998 相似文献
13.
Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems 总被引:6,自引:0,他引:6
Dan-Ping Yang. 《Mathematics of Computation》2000,69(231):929-963
Some least-squares mixed finite element methods for convection-diffusion problems, steady or nonstationary, are formulated, and convergence of these schemes is analyzed. The main results are that a new optimal a priori error estimate of a least-squares mixed finite element method for a steady convection-diffusion problem is developed and that four fully-discrete least-squares mixed finite element schemes for an initial-boundary value problem of a nonlinear nonstationary convection-diffusion equation are formulated. Also, some systematic theories on convergence of these schemes are established.
14.
Zhe Yin Hongxing Rui Qiang Xu 《Numerical Methods for Partial Differential Equations》2013,29(3):897-915
A nonlinear system of two coupled partial differential equations models miscible displacement of one incompressible fluid by another in a porous medium. A sequential implicit time‐stepping procedure is defined, in which the pressure and Darcy velocity of the mixture are approximated by a mixed finite element method and the concentration is approximated by a combination of a modified symmetric finite volume element method and the method of characteristics. Optimal order convergence in H1 and in L2 are proved for full discrete schemes. Finally, some numerical experiments are presented. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
15.
Neutral elements and central elements are characterized in different classes of posets such as sectionally semi-complemented
posets, atomistic posets etc.
相似文献
16.
XIE XiaoPing & XU JinChao School of Mathematics Sichuan University Chengdu China 《中国科学 数学(英文版)》2011,(7)
We consider mixed finite elements for the plane elasticity system and the Stokes equation. For the unmodified Hellinger-Reissner formulation of elasticity in which the stress and displacement fields are the primary unknowns, we derive two new nonconforming mixed finite elements of triangle type. Both elements use piecewise rigid motions to approximate the displacement and piecewise polynomial functions to approximate the stress, where no vertex degrees of freedom are involved. The two stress finite element ... 相似文献
17.
Chris Preston 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(1):63-71
The following is a fundamental construction in the theory of point processes: For a measurable space (X, ɛ) let X
◃ denote the set of all measures on (X, ɛ) taking only values in the set ℕ (and so each p ∈ X
◃ is a finite measure, since p(X) ∈ ℕ); put ɛ
◃ = σ(ɛ
◊), where ɛ
◊ is the set of all subsets of X
◃ having the form {p ∈ X
◃: p(E) = k} with E ∈ ɛ and k ∈ ℕ.
Dedicated to the 80th birthday of Klaus Krickeberg 相似文献
18.
HUA Dongying & WANG Lieheng The First Fundamental Department Beijing Information Technology Institute Beijing China Institute of Computational Mathematics Scientific/Engineering Computing Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2006,49(4):513-524
In this paper, we provide a new mixed finite element approximation of the varia-tional inequality resulting from the unilateral contact problem in elasticity. We use the continuous piecewise P2-P1 finite element to approximate the displacement field and the normal stress component on the contact region. Optimal convergence rates are obtained under the reasonable regularity hypotheses. Numerical example verifies our results. 相似文献
19.
Son‐Young Yi 《Numerical Methods for Partial Differential Equations》2013,29(5):1749-1777
In this article, we develop a nonconforming mixed finite element method to solve Biot's consolidation model. In particular, this work has been motivated to overcome nonphysical oscillations in the pressure variable, which is known as locking in poroelasticity. The method is based on a coupling of a nonconforming finite element method for the displacement of the solid phase with a standard mixed finite element method for the pressure and velocity of the fluid phase. The discrete Korn's inequality has been achieved by adding a jump term to the discrete variational formulation. We prove a rigorous proof of a‐priori error estimates for both semidiscrete and fully‐discrete schemes. Optimal error estimates have been derived. In particular, optimality in the pressure, measured in different norms, has been proved for both cases when the constrained specific storage coefficient c0 is strictly positive and when c0 is nonnegative. Numerical results illustrate the accuracy of the method and also show the effectiveness of the method to overcome the nonphysical pressure oscillations. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
20.
Steffen Enni 《Journal of Graph Theory》1998,27(4):213-221
We give counterexamples to two conjectures of Bill Jackson in Some remarks on arc-connectivity, vertex splitting, and orientation in graphs and digraphs (Journal of Graph Theory 12 (3):429–436, 1988) concerning orientations of mixed graphs and splitting off in digraphs, and prove the first conjecture in the (di-) Eulerian case(s). Beside that we solve a degree constrained non-uniform directed augmentation problem for di-Eulerian mixed graphs. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 213–221, 1998 相似文献