A Priori Error Analysis for NCVEM Discretization of Elliptic Optimal Control Problem

In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H1 and L2 norms. Finally, some numerical experiments are carried out to support the theoretical results.

What Is the Conformity-Nonconformity Dichotomy?

This paper argues that the conformity-nonconformity dichotomy is a false dilemma.This study first critically reviews the basic philosophical,ethical,social psychological,and pedagogical literature related to the two concepts.It then outlines the way to overcome the phenomena of conformism and nonconformism together.The description of conformity and nonconformity as deprivation of freedom becomes stronger in 20th century philosophy and special literature from Heidegger through Fischer’s definition up to Cooley,and Crutchfield.Conformity is the sinking of the Self into the Anyone,the unprincipled alignment to the opinion of group mates,and nonconformity is the unprincipled resistance to it.But what is beyond conformity and nonconformity together as a group?There is a real community,in it the transformation of our pedagogical culture in a both useful and reasonable manner to allow the youth to accept the world by denying it and to deny the world by accepting it.The real community involves the virtue of goodness.Educate for goodness,because we possibly are the honest and humane man,who disregards the sinking of the self into the anyone and the self-contained rebellion.

ACCURACY ANALYSIS FOR QUASI-WILSON ELEMENT

In this paper, it is shown that Quasi-Wilson clement possesses a very special property i.e. the consistency error is of order O(h(2)), one order higher than that of Wilson element.

A LOCKING-FREE ANISOTROPIC NONCONFORMING FINITE ELEMENT FOR PLANAR LINEAR ELASTICITY PROBLEM

The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes

A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.

Superconvergence of nonconforming finite element penalty scheme for Stokes problem using L^2 projection method

A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.

A locking-free anisotropic nonconforming rectangular finite element approximation for the planar elasticity problem

This paper deals with a new nonconforming anisotropic rectangular finite element approximation for the planar elasticity problem with pure displacement boundary condition. By use of the special properties of this element, and by introducing the complementary space and a series of novel techniques, the optimal error estimates of the energy norm and the L^2-norm are obtained. The restrictions of regularity assumption and quasi-uniform assumption or the inverse assumption on the meshes required in the conventional finite element methods analysis are to be got rid of and the applicable scope of the nonconforming finite elements is extended.

EXPLICIT ERROR ESTIMATE FOR THE NONCONFORMING WILSON'S ELEMENT

In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.

Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

This paper studies a low order mixed finite element method （FEM） for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1^4ot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H^1-norm and the pressure in the L^2-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.

Superconvergence analysis of lower order anisotropic finite element

The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. Moreover, by using the interpo- lation postprocessing technique, a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived. Numerical results are also given to verify the theoretical analysis.

Anisotropic rectangular nonconforming finite element analysis for Sobolev equations

An anisotropic rectangular nonconforming finite element method for solving the Sobolev equations is discussed under semi-discrete and full discrete schemes. The corresponding optimal convergence error estimates and superclose property are derived, which are the same as the traditional conforming finite elements. Furthermore, the global superconvergence is obtained using a post-processing technique. The numerical results show the validity of the theoretical analysis.

A streamline diffusion nonconforming finite element method for the time-dependent linearized Navier-Stokes equations

A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.

Anisotropic nonconforming Crouzeix-Raviart type FEM forsecond-order elliptic problems

The nonconforming Crouzeix-Raviart type linear triangular finite element approximate to second-order elliptic problems is studied on anisotropic general triangular meshes in 2D satisfying the maximal angle condition and the coordinate system condition. The optimal-order error estimates of the broken energy norm and L2-norm are obtained.

New nonconforming finite element method for solving transient Naiver-Stokes equations

For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., pNC/pNC triangular and pNQ/pNQ quadrilateral finite element spaces. The semi- and full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features： avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.

The Energy-orthogonal Tetrahedral Finite Element for Fourth Order Elliptic Equations

In this paper,the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three spatial dimensions.The newly constructed element is proved to be convergent for a model biharmonic equation.

Increased Cortical Thickness in Male-to-Female Transsexualism

Background: The degree to which one identifies as male or female has a profound impact on one’s life. Yet, there is a limited understanding of what contributes to this important characteristic termed gender identity. In order to reveal factors influencing gender identity, studies have focused on people who report strong feelings of being the opposite sex, such as male-to-female (MTF) transsexuals. Method: To investigate potential neuroanatomical variations associated with transsexualism, we compared the regional thickness of the cerebral cortex between 24 MTF transsexuals who had not yet been treated with cross-sex hormones and 24 age-matched control males. Results: Results revealed thicker cortices in MTF transsexuals, both within regions of the left hemisphere (i.e., frontal and orbito-frontal cortex, central sulcus, perisylvian regions, paracentral gyrus) and right hemisphere (i.e., pre-/post-central gyrus, parietal cortex, temporal cortex, precuneus, fusiform, lingual, and orbito-frontal gyrus). Conclusion: These findings provide further evidence that brain anatomy is associated with gender identity, where measures in MTF transsexuals appear to be shifted away from gender-congruent men.

A Locking-free Nonconforming Finite Element for Planar Linear Elasticity

We propose a locking-free nonconforming finite element method to solve for the displacement variation in the pure displacement boundary value problem of planar linear elasticity. The method proposed in this paper is robust and optimal, in the sense that the convergence estimate in the energy is independent of the Lame parameter λ.

A SUPERCONVERGENT ESTIMATE OF WILSON-LIKE ELEMENTS

In this paper, the supercouvergence of a class of Wilson-like elements is considered, and a superconvergent estimate of Wilson-like elements is obtained for strong regular meshes.

AN OPTIMAL V-CYCLE MULTIGRID METHOD FOR CONFORMING AND NONCONFORMING PLATE ELEMENTS

In this paper, an optimal V-cycle multigrid method for some conforming and nonconforming plate elements are constructed. A new method dealing with nonnested multigrid methods is presented.