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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 85 (2000), S. 503-524 
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65N30, 65N12
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. Interpolation error estimates for a modified 8-node serendipity finite element are derived in both regular and degenerate cases, the latter of which includes the case when the element is of triangular shape. For $u \in W^{3, p}(K)$ defined over a quadrilateral K, the error for the interpolant $\Pi_K u$ is estimated as $|u-\Pi_K u|_{W^{\alpha, p}(K)}\le Ch^{3-\alpha}_K|u|_{W^{3,p}(K)}$ $(\alpha=0, 1)$ , where $1 \le p \le +\infty$ in the regular case and $1\le p 〈 3$ in the degenerate case, respectively. Thus, the obtained error estimate in the degenerate case is of the same quality as in the regular case at least for $1\le p〈3$ . Results for some related elements are also given.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 24 (1975), S. 211-231 
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A justification of a finite element scheme for plate bending problems is presented. The finite element treated here is the triangular element proposed by Stricklinet al. and Dhatt using the discrete Kirchhoff assumption. Some error estimates are derived for the finite element solutions of static and eigenvalue problems with the homogeneous Dirichlet conditions. Numerical experiments are also performed to see the validity of the theory.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 23 (1999), S. 240-249 
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Molecular genetics and genomics 233 (1992), S. 209-216 
    ISSN: 1617-4623
    Keywords: Transposable element ; Retrotransposon ; Reverse transcriptase ; Rice ; Polymerase chain reaction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary Three families of retrotransposons of rice (Tos1,Tos2, andTos3) were isolated by using a method based on the sequence conservation of the primer binding site for reverse transcription. This method should be generally applicable for cloning retrotransposons of other plants. One retrotransposon,Tos3-1, was studied in detail.Tos3-1 is 5.2 kb long, has structures common to retrotransposons, such as long terminal repeats (LTR), a primer binding site complementary to the initiator tRNA, a polypurine tract, and generates target sequence duplications flanking the inserted element. Southern blotting analysis showed that sequences homologous toTosl, 2 and3 are found in wild rice species as well as in cultivated rice species, but not in maize and tobacco. The copy number and genomic location of the families vary in different strains of one species of wild rice, suggesting that these elements may still be active. Retrotransposons were also screened for by amplification of the reverse transcriptase coding region using the polymerase chain reaction (PCR). At least two types of copia-like elements (Tos4] andTos5) were found. The total copy number of retrotransposons in the rice genome was estimated to be about 1000. These results suggest that, as inDrosophila, retrotransposons are the major transposon class in rice.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 115-122 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents theory and examples of partial approximation as a modification of the displacement method in the finite element analysis. This method requires different shape functions for different terms in the potential energy expression to curtail the processes in the standard displacement method. Explanation of the theory is given by use of a simple example for Poisson's equation. It can also be effectively utilized to give mathematical foundation to some finite element models based on physical reasonings, such as Melosh's rectangular element for plate bending and beam element approximation of circular arches.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 39-54 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a general theory and application of the finite element method for some special class of non-self-adjoint problems. The formulation employed here is based on the Galerkin method for linear boundary value and eigenvalue problems described by the partial differential equations of elliptic type, and it can be regarded as an extension of the usual displacement method formulated by the use of the principle of minimum potential energy. In order to illustrate its validity and feasibility, the method is applied to the problems of the two-group neutron diffusion equations and of the stability of a non-conservative system.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 711-716 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We derive explicit expressions of shape functions for the 8-node serendipity element with bilinear element geometry, which is modified so that it can represent any quadratic fields in Cartesian co-ordinates. The modification is similar to the one by MacNeal and Harder, but is slightly different and based on our own idea. We also show that the usual 6-node triangular element can be obtained by applying the node degeneration technique to this modified element.
    Additional Material: 1 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 98-122 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The aim of this work is to give theoretical justification of several types of finite element approximations to the initial-boundary value problems of first order linear hyperbolic equations. Our approximate scheme is obtained by the piecewise linear continuous finite element method for space variable, x, and the Euler type step by step integration method for time variable, t. An artificial viscosity technique, up-stream type methods are considered within the frame work of L2-theory. The convergence and the error estimate of the approximate solutions to the true one are discussed.
    Additional Material: 2 Ill.
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  • 9
    Publication Date: 1975-06-01
    Print ISSN: 0029-599X
    Electronic ISSN: 0945-3245
    Topics: Mathematics
    Published by Springer
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  • 10
    Publication Date: 2000-05-01
    Print ISSN: 0029-599X
    Electronic ISSN: 0945-3245
    Topics: Mathematics
    Published by Springer
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