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  • 1
    Electronic Resource
    Electronic Resource
    On a certain two-sided symmetric condition in magnetic field analysis and computations (1997)
    Springer
    Applications of mathematics 42 (1997), S. 147-159 
    Details
    ISSN: 1572-9109
    Keywords: magnetic field ; variational formulation ; two-sided existence and uniqueness condition ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity models used in electrotechnical practice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022295111737
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  • 2
    Electronic Resource
    Electronic Resource
    Towards adaptive finite element schemes for partial differential Volterra equation solvers (1996)
    Springer
    Advances in computational mathematics 6 (1996), S. 309-323 
    Details
    ISSN: 1572-9044
    Keywords: finite element method ; discontinuous Galerkin method ; a posteriori error estimates ; adaptivity ; Volterra equations ; viscoelasticity ; 45K05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a brief indication of how elliptic, parabolic and hyperbolic partial differential equations with memory arise when modelling viscoelastic materials. We then point out the urgent need for adaptive solvers for these problems and, employing the methodology of Eriksson, Johnson et al. (e.g., SIAM J. Numer. Anal. 28 (1991)), we given ana posteriori error estimate for a model two-point hereditary boundary value problem. The strengths and weaknesses of the analysis and estimate are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02127710
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  • 3
    Electronic Resource
    Electronic Resource
    Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method (1997)
    Springer
    Applications of mathematics 42 (1997), S. 259-277 
    Details
    ISSN: 1572-9109
    Keywords: Parameter identification ; parabolic problem ; finite element method ; Crank-Nicolson scheme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023012328209
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  • 4
    Electronic Resource
    Electronic Resource
    A review of two different approaches for superconvergence analysis (1998)
    Springer
    Applications of mathematics 43 (1998), S. 401-411 
    Details
    ISSN: 1572-9109
    Keywords: finite element method ; superconvergence error estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In 1995, Wahbin presented a method for superconvergence analysis called “Interior symmetric method,” and declared that it is universal. In this paper, we carefully examine two superconvergence techniques used by mathematicians both in China and in America. We conclude that they are essentially different.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023220520477
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  • 5
    Electronic Resource
    Electronic Resource
    A finite element convergence analysis for 3D Stokes equations in case of variational crimes (2000)
    Springer
    Applications of mathematics 45 (2000), S. 99-129 
    Details
    ISSN: 1572-9109
    Keywords: Stokes equations ; nonstandard boundary conditions ; finite element method ; approximation of boundary
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022235512626
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  • 6
    Electronic Resource
    Electronic Resource
    Correction of finite element eigenvalues for problems with natural or periodic boundary conditions (1988)
    Springer
    BIT 28 (1988), S. 254-269 
    Details
    ISSN: 1572-9125
    Keywords: 65L15 ; 65L60 ; asymptotic correction ; Sturm-Liouville eigenvalues ; finite element method ; natural boundary conditions ; periodic boundary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recent results of Andrew and Paine for a regular Sturm-Liouville problem with essential boundary conditions are extended to problems with natural or periodic boundary conditions. These results show that a simple asymptotic correction technique of Paine, de Hoog and Anderssen reduces the error in the estimate of thekth eigenvalue obtained by the finite element method, with linear hat functions and mesh lengthh, fromO(k 4 h 2) toO(kh 2). Numerical results show the correction to be useful even for low values ofk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01934090
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  • 7
    Electronic Resource
    Electronic Resource
    A framework for advancing front techniques of finite element mesh generation (1995)
    Springer
    BIT 35 (1995), S. 210-232 
    Details
    ISSN: 1572-9125
    Keywords: Unstructured meshes ; finite element method ; Delaunay triangulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Advancing front techniques are a family of methods for finite element mesh generation that are particularly effective in dealing with complicated boundary geometries. In the first part of this paper, conditions are presented which ensure that any planar aft algorithm that meets these conditions terminates in a finite number of steps with a valid triangulation of the input domain. These conditions are described by specifying a framework of subtasks that can accommodate many aft methods and by prescribing the minimal requirements on each subtask that ensure correctness of an algorithm that conforms to the framework. An important efficiency factor in implementing an aft is the data structure used to represent the unmeshed regions during the execution of the algorithm. In the second part of the paper, we discuss the use of the constrained Delaunay triangulation as an efficient abstract data structure for the unmeshed regions. We indicate how the correctness conditions of the first part of the paper can be met using this representation. In this case, we also discuss the additional requirements on the framework which ensure that the generated mesh is a constrained Delaunay triangulation for the original boundary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01737163
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  • 8
    Electronic Resource
    Electronic Resource
    Ultrasonic beam propagation through a bimetallic weld—A comparison of predictions of the Gauss-Hermite beam model and finite element method (1993)
    Springer
    Journal of nondestructive evaluation 12 (1993), S. 151-158 
    Details
    ISSN: 1573-4862
    Keywords: Beam propagation ; bimetallic weld ; Gauss-Hermite beam model ; finite element method ; ultrasonics ; anisotropic medium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract In this paper, predictions of two models for the propagation of ultrasonic beams through a two-dimensional, bimetallic weld geometry are compared. The finite element method can predict beam propagation through quite general geometry with high accuracy. This model, however, requires significant computational time. On the other hand, the approximate Gauss-Hermite model offers considerably greater computational speed, but has lower accuracy in certain regions and cannot treat the most general geometries and inhomogeneities in material properties. This paper compares the performances of the two models for the case of the two-dimensional, bimetallic weld consisting of multiple layers, some of which have anisotropic properties. It is found that the results of the two models are in good agreement in the vicinity of the central ray, and that the deviation increases as one moves away from the axis. Also, as the beam propagates through multiple interfaces, the accuracy of the Gauss-Hermite solution decreases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00567571
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  • 9
    Electronic Resource
    Electronic Resource
    Identification of crack size via an energy approach (1994)
    Springer
    Journal of nondestructive evaluation 13 (1994), S. 1-11 
    Details
    ISSN: 1573-4862
    Keywords: Crack detection ; modal testing ; nondestructive evaluation ; fracture mechanics ; structure ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract An energy method for identifying the size of a crack at given location in structures using one measured eigencouple of the cracked structures is presented. The method utilizes the maximum strain energies of the structures both with and without a crack and the additional strain energy induced by the crack to construct the energy balance equation from which the size of the crack is evaluated through an iteration procedure. A pair of measured vibration frequency and mode shape of the cracked structure is used in a free vibration analysis to derive for its maximum strain energy. The maximum inertia force of the cracked structure is then applied to the uncracked structure with known stiffness and the resulting strain energy of the uncracked structure is obtained in a finite element analysis. Fracture mechanics is used to derive for the additional strain energy induced by the crack. Experimental investigations of several cracked free-free beams are performed to validate the proposed method. Examples of the identification of crack sizes for a number of damaged beam structures are given to further illustrate the feasibility and effectiveness of the present method. Overall the results are encouraging showing that the present method has the prospect of becoming an alternative approach for crack size detection.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00723942
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  • 10
    Electronic Resource
    Electronic Resource
    Analysis of discrete techniques for image transformation (1996)
    Springer
    Numerical algorithms 13 (1996), S. 225-263 
    Details
    ISSN: 1572-9265
    Keywords: numerical integration ; error analysis ; harmonic transformation ; finite element method ; digital image ; image transformation ; 65N15 ; 65D30 ; 68A45
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Let an image be distorted by a nonlinear transformationT, and then be restored back to its original by the inverse transformationT −1. Such a cycle conversion,T −1 T, of digital images can be facilitated by the combination (CSIM) given in [6] using the splitting-shooting method and the splitting-integrating method forT andT −1 respectively. Since there is no need to solve nonlinear equations, CSIM has been widely applied to specific areas of image processing and pattern recognition, even those with complicated transformations, e.g., the harmonic transformation [12]; however, no strict error analysis has been provided so far. In this paper, a priori error estimates and convergence rates are derived for pixel greyness obtained from CSIM; also the analytical results are extended to the harmonic transformation. Numerical and graphical experiments are provided to support the theoretical analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02207696
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