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  • Books
  • Articles  (158)
  • finite element method  (145)
  • rationality
  • Mathematics  (150)
  • Sociology  (8)
  • 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
    Rationality and the definition of consistent pairs (1998)
    Springer
    International journal of game theory 27 (1998), S. 49-59 
    Details
    ISSN: 1432-1270
    Keywords: Key words: Consistent pairs ; rationality ; lexicographic probability systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. A consistent pair specifies a set of “rational” strategies for both players such that a strategy is rational if and only if it is a best reply to a Bayesian belief that gives positive probability to every rational strategy of the opponent and probability zero otherwise. Although the idea underlying consistent pairs is quite intuitive, the original definition suffers from non-existence problems. In this article, we propose an alternative formalization of consistent pairs. According to our definition, a strategy is “rational” if and only if it is a best reply to some lexicographic probability system that satisfies certain consistency conditions. These conditions imply in particular that a player's probability system gives infinitely more weight to rational strategies than to other strategies. We show that modified consistent pairs exist for every game.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001820050057
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  • 9
    Electronic Resource
    Electronic Resource
    Rationality and the definition of consistent pairs (1998)
    Springer
    International journal of game theory 27 (1998), S. 49-59 
    Details
    ISSN: 1432-1270
    Keywords: Consistent pairs ; rationality ; lexicographic probability systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A consistent pair specifies a set of “rational” strategies for both players such that a strategy is rational if and only if it is a best reply to a Bayesian belief that gives positive probability to every rational strategy of the opponent and probability zero otherwise. Although the idea underlying consistent pairs is quite intuitive, the original definition suffers from non-existence problems. In this article, we propose an alternative formalization of consistent pairs. According to our definition, a strategy is “rational” if and only if it is a best reply to some lexicographic probability system that satisfies certain consistency conditions. These conditions imply in particular that a player's probability system gives infinitely more weight to rational strategies than to other strategies. We show that modified consistent pairs exist for every game.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01243194
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  • 10
    Electronic Resource
    Electronic Resource
    The survival value of assuming others to be rational (2000)
    Springer
    International journal of game theory 29 (2000), S. 147-163 
    Details
    ISSN: 1432-1270
    Keywords: Key words: Evolutionary psychology ; rationality ; beliefs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. I study the evolution of rationality, using an indirect evolutionary approach, in which nature selects a decision-making procedure, and the procedure chooses actions in matching-games. The main result is that in order for (knowledge of) rationality to survive, it is necessary and sufficient that the rational procedure respects the attraction principle. That is, when a rational agent eliminates a strictly dominated action A, he should only increase the choice probability of the actions actually dominating A and not change the choice probability of other undominated actions. The attraction principle sharpens gametheoretic predictions. Attraction effects have been verified in psychological experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001820070001
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