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.

CALCULATION OF MILL RIGIDITY BY THREE DIMENSION CONTACT BOUNDARY ELEMENT METHOD

Vertical rigidity of the space self adaptive 530 high rigidity mill is calculated by applying the boundary element method (BEM) of three dimension elastic contact problem,which can update the existed deforming separation calculating theory and corresponding methods of material mechanics,elastic mechanics and finite element method.The method has less hypotheses and stronger synthesis in contact type calculating model.The advantages of the method are high calculating rate,high calculating accuracy,etc..

Evaluation on abundance or deficiency of avai－lable trace elements in soil of middle area in China and the effect of applying trace element fertilizer

The authors selected the west part of Xinxiang City,Henan Province in the north China plain as a typical region and carried out assessments of the abundanca or deficiency of the trace ele- ments(B,Mn,Mo,Zn,Cu,Fe)in soil.It can be seen from results that more than 80% of the farmland is deficiency of zinc(<1.0ppm),40% of molybdenum(0.15ppm),38% of boron(0.5ppm),29% of manganese(100ppm)and 13% of iron(7.0ppm)and that the content of available trace ele- ments in soil are related to the topography closely.Next the proper application of trace elements on grain crops is presented.

The sediments of lake on the Ardley Island, Antarctica: Identification of penguin-dropping soil

During CHINARE 15(Dec. 1998 Mar. 1999), a lake core 67.5 cm in length, was sampled in Y2 lake, which is located on the Ardley Island, Antarctica. The concentrations of some chemical elements in Y2 lake sediments were analyzed. According to comparative research on elementary characters of sediments in Antarctic West Lake, fresh penguin dropping as well as guano soil on the Ardley Island and Pacific Island in South China Sea, it presents that the Y2 lake sediments were ameliorated by penguin dropping. The result of element cluster analysis shows that the type elements in the sediment impacted by penguin dropping include Sr,F,S,P,Ca,Se,Cu,Zn and Ba. This can provide a base for further interpreting the climatic and environmental event recorded in the sediment.

Comparisons in finite element analysis of minimally invasive, locking,and non-locking plates systems used in treating calcaneal fractures of Sanders type Ⅱ and type Ⅲ

Background Calcaneal fractures are relatively common but complex,while the treatment of these fractures is still controversial.The objective of this study was to compare the biomechanical stability of minimally invasive,locking,and non-locking plating systems used for fixing Sanders type Ⅱ and type Ⅲ calcaneal fractures.Finite element analysis was used for comparing the three types of plating systems.This study helped in guiding the clinical management of calcaneal fractures.Methods The CT data acquired from a volunteer was used to construct a finite element model of calcaneus.The fracture lines were made according to Sanders type Ⅱ （A,B,C） and type Ⅲ （AB,AC,BC） and six calcaneal fractures models were constructed accordingly.Three fixation methods used in clinical treatment were simulated by design tools （minimally invasive plating with percutaneous screws,Y-size non-locking plating,and locking plating） and then fixed to these fracture models with the help of clinical principles.The single minimally invasive plating fixation was also tested to compare the function of percutaneous screws.Then,the neutral force was applied on established methods.The displacement and presses distribution condition in various plating models were analyzed and compared.Results The levels of displacement and compressive press on the bone around fixation or strains on plating were within the physiological limit,indicating that the three methods were suitable for application.Compared with the locked and unlocked plates,the minimally invasive plating caused a relatively lower displacement without the high stress in bone or fixation.The minimum stress in fixation was observed in locking plate as the distribution of stress was concentrated in the anterior part of locking plate.Conclusions The minimally invasive plating method could be a better alternative method in treating Sanders type Ⅱ and type Ⅲ calcaneal fractures.The observed stiffness of locking plate was not obviously stronger than unlocked plate.

ANISOTROPIC CROUZEIX-RAVIART TYPE NONCONFORMING FINITE ELEMENT METHODS TO VARIATIONAL INEQUALITY PROBLEM WITH DISPLACEMENT OBSTACLE

In this paper, anisotropic Crouzeix-Raviart type nonconforming finite element meth- ods are considered for solving the second order variational inequality with displacement obstacle. The convergence analysis is presented and the optimal order error estimates are obtained under the hypothesis of the finite length of the free boundary. Numerical results are provided to illustrate the correctness of theoretical analysis.