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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3585-3603 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a postprocessed type of a posteriori error estimate and a h-version adaptive procedure for the semidiscrete finite element method in dynamic analysis. In space the super-convergent patch recovery technique is used for determining higher-order accurate stresses and, thus, a spatial error estimate. In time a postprocessing technique is developed for obtaining a local error estimate for one step time integration schemes (the HHT-α method). Coupling the error estimate with a mesh generator, a h-version adaptive finite element procedure is presented for two-dimensional dynamic analysis. It updates the spatial mesh and time step automatically so that the discretization errors are controlled within specified tolerances. Numerical studies on different problems are presented for demonstrating the performances of the proposed adaptive procedure.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2131-2152 
    ISSN: 0029-5981
    Keywords: discontinuous Galerkin finite element method ; predictor-multicorrector ; adaptive time integration ; structural dynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper studies a time-discontinuous Galerkin finite element method for structural dynamic problems, by which both displacements and velocities are approximated as piecewise linear functions in the time domain and may be discontinuous at the discrete time levels. A new iterative solution algorithm which involves only one factorization for each fixed time step size and a few iterations at each step is presented for solving the resulted system of coupled equations. By using the jumps of the displacements and the velocities in the total energy norm as error indicators, an adaptive time-stepping procedure for selecting the proper time step size is described. Numerical examples including both single-DOF and multi-DOF problems are used to illustrate the performance of these algorithms. Comparisons with the exact results and/or the results by the Newmark integration scheme are given. It is shown that the time-discontinuous Galerkin finite element method discussed in this study possesses good accuracy (third order) and stability properties, its numerical implementation is not difficult, and the higher computational cost needed in each time step is compensated by use of a larger time step size.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 273-292 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher-order one which assumes that the derivatives of accelerations vary linearly within each time step. It may be obtained directly without resolving new equations, so the additional computational cost is small and the implementation is convenient. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post-processing technique. Accordingly, an adaptive time-stepping procedure, which automatically adjusts the time-step size so that the local error at each time step is within a prescribed accuracy, is described. Numerical examples, including two single-DOF problems, a two-DOF problem and a multi-DOF model, are presented. The results show that the presented local error estimator is simple, reliable and accurate.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 313-320 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Publication Date: 2014-05-21
    Description: Atmospheric particle pollution is a serious environmental issue in China, especially the northern regions. Ambient air loadings (ng m−3), pollution sources and apportionment, and transport pathways of trace (Cd, Co, Cu, Ni, Pb, V, and Zn) and major (Al, Ca, Fe, and Mg) metals associated with inhalable particulate matters (PM10 aerosols) were characterized in urban, rural village, and rural field areas of seven cities (from inland in the west to the coast in the east: Wuwei, Yinchuan, Taiyuan, Beijing, Dezhou, Yantai, and Dalian) across northern China by taking one 72 h sample each site within a month for a whole year (April 2010 to March 2011). Ambient PM10 pollution in northern China is especially significant in the cold season (October–March) due to the combustion of coal for heating and dust storms in the winter and spring. Owing to variations in emission intensity and meteorological conditions, there is a trend of decrease in PM10 levels in cities from west to east. Both air PM10 and the associated metal loadings for urban and rural areas were comparable, showing that the current pattern of regional pollution in China differs from the decreasing urban–rural-background transect that is usual in other parts of the world. The average metal levels are Zn (276 ng m−3) ≫ Pb (93.7) ≫ Cu (54.9) ≫ Ni (9.37) 〉 V (8.34) ≫ Cd (2.84) 〉 Co (1.76). Judging from concentrations (mg kg−1), enrichment factors (EFs), a multivariate statistical analysis (principal component analysis, PCA), and a receptor model (absolute principal component scores-multiple linear regression analysis, APCS-MLR), the airborne trace metals (Zn, Pb, Cu, and Cd) in northern China were mainly anthropogenic, and mostly attributable to coal combustion and vehicle emissions with additional industrial sources. However, the Co was mostly of crustal origin, and the V and Ni were mainly from soil/dust in the western region and mostly from the petrochemical industry/oil combustion in the east. The accumulation of typical "urban metals" (Pb, Zn, Cd, and Cu) showed a trend of increase from west to east, indicating their higher anthropogenic contribution in eastern cities. The winter northwestern monsoon and westerly jet stream were the dominant forces in the long-range transport of airborne PM metals in northern China, with potentially global implications.
    Electronic ISSN: 1680-7375
    Topics: Geosciences
    Published by Copernicus on behalf of European Geosciences Union.
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