Top PDF Exact a posteriori error analysis of the least squares finite element method

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 e€ective 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

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 H 1 -norm and in the L 2 -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.

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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]

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 suciently 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.

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.

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.

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]

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.

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.

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]

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]

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

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.

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.