Abstract
**A** residual type **a** **posteriori** **error** estimator is presented for **the** **least** **squares** ®nite **element** **method**. **The** estimator is proved to equal **the** **exact** **error** in **a** norm induced by some **least** **squares** functional. **The** **error** indicator **of** each **element** is equal to **the** **exact** **error** norm restricted to **the** **element** as well. In other words, **the** estimator is perfectly eective and reliable for **error** control and for adaptive mesh re®nement. **The** exactness property requires virtually no assumptions on **the** regularity **of** **the** solution and on **the**

Show more
19 Read more

PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure **the** accuracy **of** all **the** information (**the** “Content”) contained in **the** publications on our platform. However, Taylor & Francis, our agents, and our licensors make no
representations or warranties whatsoever as to **the** accuracy, completeness, or suitability for any purpose **of** **the** Content. Any opinions and views expressed in this publication are **the** opinions and views **of** **the** authors, and are not **the** views **of** or endorsed by Taylor & Francis. **The** accuracy **of** **the** Content should not be relied upon and should be independently verified with primary sources **of** information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out **of** **the** use **of** **the** Content.

Show more
A general framework of the theoretical analysis for the convergence and stability of the standard least squares finite element approximations to boundary value problems of fir[r]

12 Read more

b Department **of** Statistics, Ming Chuan University, Taipei 11120, Taiwan, ROC
c Department **of** Applied Mathematics, I-Shou University, Ta-Hsu, Kaohsiung 84008, Taiwan, ROC
Abstract
In this paper **a** **least**-**squares** ®nite **element** **method** for **the** Timoshenko beam problem is proposed and analyzed. **The** **method** is shown to be convergent and stable without requiring extra smoothness **of** **the** **exact** solutions. For suciently regular **exact** solutions, **the** **method** achieves optimal order **of** convergence in **the** H 1 -norm for all **the** unknowns (displacement, rotation, shear, moment), uniformly in **the** small parameter which is generally proportional to **the** ratio **of** thickness to length. Thus **the** locking phenomenon disappears as **the** parameter tends to zero. **A** sharp **a** **posteriori** **error** es- timator which is **exact** in **the** energy norm and equivalent in **the** H 1 -norm is also brie¯y discussed. Ó 2000 Published by Elsevier Science Inc. All rights reserved.

Show more
13 Read more

Taylor & Francis makes every effort to ensure **the** accuracy **of** all **the** information (**the** “Content”) contained in **the** publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to **the** accuracy, completeness, or suitability for any purpose **of** **the** Content. Any opinions and views expressed in this publication are **the** opinions and views **of** **the** authors, and are not **the** views **of** or endorsed by Taylor & Francis. **The** accuracy **of** **the** Content should not be relied upon and should be independently verified with primary sources **of** information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out **of** **the** use **of** **the** Content.

Show more
19 Read more

PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure **the** accuracy **of** all **the** information (**the** “Content”) contained in **the** publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to **the** accuracy, completeness, or suitability for any purpose **of** **the** Content. Any opinions and views expressed in this publication are **the** opinions and views **of** **the** authors, and are not **the** views **of** or endorsed by Taylor & Francis. **The** accuracy **of** **the** Content should not be relied upon and should be independently verified with primary sources **of** information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out **of** **the** use **of** **the** Content.

Show more
24 Read more

These methods offer certain advantages such as that they need not satisfy the inf-sup condition which is required in the mixed finite element formulation, that a sin[r]

22 Read more

Compared to **the** cost **of** computing **the** approximate solution u h , **the** cost **of** computing **the** es- timated **error** ˜e is fractional since **the** complementary BE space S h c can be constructed using, for instance, only one or two shape functions on each **element**. Consequently, we only have one or two equations in **the** solution **of** **a** local problem. In particular, if only one shape function is used for S h c , our estimator is then equivalent to **the** previous residual **error** estimators; see **the** numerical ex- ample for **a** hypersingular integral equation presented in Section 4. Furthermore, since **the** estimated **error** is explicitly calculated there is no restriction on **the** choice **of** **the** norm used to measure **the** errors. In other words, whichever **the** norm appropriate for **the** approximate solution u h can also be used for **the** estimated **error** ˜e. This can be very useful in practice when **a** more
exible norm is needed for assessing **the** computed solution. We however only prove estimate (1.1) in **the** energy norm.

Show more
19 Read more

Department **of** Electronics Engineering and Institute **of** Electronics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan Received 25 May 1998; received in revised form 5 January 2000
Abstract
This paper proposes **a** new algorithm for designing "nite word length linear-phase FIR "lters. **The** new algorithm produces "nite-precision **least**-**squares** **error** (LSE) solutions with much reduced search time than **the** brute-force full search algorithm. It is di!erent from **the** full search algorithm that tries all possible combinations directly. **The** new algorithm utilizes geometric properties **of** **a** hyper-space to pinpoint potential solutions in **a** much more restricted way.

Show more
In the finite element model, we need to establish the planar coil, the core, the magnetic material block and the substance between the two (it will be air in the present analysis). We us[r]

10 Read more

On the other hand, an attempt to create a univer- sal conditions for the general system (1) and (2) in the context of LSFE approx- imation is very intractable if not impossi[r]

19 Read more

Numerical results, including the frequency response and the dependence on the period number of the scattering parameters, for finite periodic structures in dielectric-load[r]

Hz。本研究結果顯示，利用自然頻率為參數作為評估人工牙根邊界骨高度或邊 界骨質密度，是可信且可行的。
Abstract
For years, radiographic examination has been **the** main clinical **method** for **the** assessment **of** **the** dental implant in vivo condition. However, **the** use **of** such **method** is limited for many applications due to its low sensitivity. As **a** result, it is thus difficult to diagnose in **the** early stages **of** bone losses. Therefore, there is **a** strong clinical demand for **a** novel non-invasive technique to evaluate objectively **the** status **of** **the** dental implant under various bone qualities. Thus, **the** goal **of** current study is to provide **a** preliminary

Show more
Keywords: Residual stress, Blind-hole **method**, Hole-drilling **method**, **Finite** **element** **method**
Abstract. This study investigates **the** effectiveness **of** **the** hole-drilling strain gage **method** on residual stress estimation. **The** thermal-elastic-plastic model **of** **the** commercial Marc **finite** **element** **method** package is used to simulate and build up **the** hole-drilling process and residual stress distribution.

Finite Element Solution of Boundary Value Problems By O. Barker[r]

Finite Element Solution of Boundary Value Problems By O. Barker[r]

Aspects to consider for sufficient bone support are primary cortical anchorage and healing time before loading **the** implants. Reliance on **the** existing cortical bone seems to be **the** most predictable condi- tion. This means great care must be taken to preserve any available outer cortex in **the** posterior regions for anchorage **of** implant threads. **The** different thick- nesses **of** cortical bone between **the** buccal and lin- gual sides may affect **the** prognosis **of** implant. In **the** same force but in **the** opposing direction, **the** thicker **the** cortical bone, **the** more **the** peak value **of** stress.

Show more
The purpose of this paper is t o design linear phase FIR filters using total least squares (TLS) error criterion which has been successfully used to solve many engineeri[r]

Here, we have developed an efficient **method** for evolving QSAR models by intro- ducing **a** number **of** successive refinements which can be summarized as follows: 1) An extra bit lv, representing **the** number **of** latent variables, was appended to **the** chromosome **of** GA and expected to efficiently solve **the** problem **of** **the** optimum number **of** latent variables though evolutionary process; 2) Mahalanobis distance was adopted to select significant features from numerous features from COMBINE; 3) **A** new genetic operator, called biased mutation, was designed to lead **the** evolution **of** GA toward significant feature set and to reduce **the** interference **of** noise features. In this paper, we proposed **a** new QSAR **method** by integrating **a** generic evolutionary **method**, modified and enhanced from our previous works 9,10 and above issues, and PLS (GEMPLS). GEMPLS is general able to evolve **the** relationship between biologi- cal activities and compound features generated by other methods, such as CoMFA and COMBINE. Here we applied GEMPLS to evolve **the** QSAR models according to **the** interaction energy features generated by **the** COMBINE **method** on 48 HIV-1 pro- tease inhibitors. Experiments show that GEMPLS is able to improve **the** predictability and efficiency, at **the** same time, **the** selected residues in **the** yielded QSAR model are consistent with some experimental evidences.

Show more
11 Read more