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  • Articles  (14)
  • Other Sources
  • CR: G1.8  (14)
  • Springer  (14)
  • American Chemical Society
  • 1995-1999
  • 1985-1989  (14)
  • 1970-1974
  • 1985  (14)
  • Mathematics  (14)
  • Technology
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
  • Energy, Environment Protection, Nuclear Power Engineering
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  • Articles  (14)
  • Other Sources
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  • Springer  (14)
  • American Chemical Society
Years
  • 1995-1999
  • 1985-1989  (14)
  • 1970-1974
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  • Mathematics  (14)
  • Technology
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
  • Energy, Environment Protection, Nuclear Power Engineering
  • 1
    Electronic Resource
    Electronic Resource
    Control of stefan problems by means of linear-quadratic defect minimization (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 429-442 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65P05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We investigate the following problem: To influence a heat conduction process in such a way that the conductor melts in a prescribed manner. Since we treat a linear auxiliary problem, it suffices to deal with a linear-quadratic defect minimization problem with linear restrictions, where we use splines or polynomials as approximation spaces. In case of exact controllability we derive various order of convergence estimates, which we discuss for some numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389495
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  • 2
    Electronic Resource
    Electronic Resource
    A finite element lumped mass scheme for solving eigenvalue problems of circular arches (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 499-504 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This study is a continuation of a previous paper [4] in which the numerical results are given by using single precision arithmetic. In this paper, we show the numerical results which experess the sharper convergence properties than those of [4], by using double precision arithmetic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389655
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  • 3
    Electronic Resource
    Electronic Resource
    On finite element approximation in theL ∞-norm of variational inequalities (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 45-57 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS)-65N30, 49D20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We are interested in the approximation in theL ∞-norm of variational inequalities with non-linear operators and somewhat irregular obstacles. We show that the order of convergence will be the same as that of the equation associated with the non-linear operator if the discrete maximum principle is verified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389875
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  • 4
    Electronic Resource
    Electronic Resource
    Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 139-157 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A semidiscrete Galerkin finite element method is defined and analyzed for nonlinear evolution equations of Sobolev type in a single space variable. Optimal orderL p error estimates are derived for 2≦p≦∞. And it is shown that the rates of convergence of the approximate solution and its derivative are one order better than the optimal order at certain spatial Jacobi and Gauss points, respectively. Also the standard nodal superconvergence results are established. Futher, it is considered that an a posteriori procedure provides superconvergent approximations at the knots for the spatial derivatives of the exact solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389881
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  • 5
    Electronic Resource
    Electronic Resource
    Approximation of a bending plate problem with a boundary unilateral constraint (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 435-458 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study a variational formulation of the unilaterally supported bent plate problem and we analyze the approximation of the problem by a mixed finite element method. We proveO(h) andO(h|lnh|1/2) error bounds respectively for the moments and the displacement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389591
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  • 6
    Electronic Resource
    Electronic Resource
    Sur les éléments finis rationnels de Serendip de degré quelconque (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 175-187 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A general construction of rational finite elements of serendip type on convex quadrilaterals is described in this paper. A first technique consists in eliminating formerly introduced nodes; a second possibility is to use the transformation of Coxeter-Wachspress. Error bounds are given for the associate interpolation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390418
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  • 7
    Electronic Resource
    Electronic Resource
    W m,2 -Fehlerabschätzungen für Galerkin-Näherungen schwach elliptischer quasilinearer Randwertprobleme 2m-ter Ordnung (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 597-609 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65N15 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For weak elliptic quasilinear boundary value problems of order 2m inn dimensionsW m,2 -error estimates for the Galerkin method are established, in whichL ∞-norms of certain derivatives of the Galerkin approximations still occur. The order of these derivatives depends on several conditions on the coefficients of the differential operator. With the help of appropriate a priori bounds for the discrete solutions asymptotic error estimates for the finite element method may be obtained from this. This procedure yields quasioptimal results in several cases. Finally some examples are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389459
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  • 8
    Electronic Resource
    Electronic Resource
    On some boundary element methods for the heat equation (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 101-120 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The object of this paper is to study some boundary element methods for the heat equation. Two approaches are considered. The first, based on the heat potential, has been studied numerically by previous authors. Here the convergence analysis in one space dimension is presented. In the second approach, the heat equation is first descretized in time and the resulting elliptic problem is put in the boundary formulation. A straight forward implicit method and Crank-Nicolson's method are thus studied. Again convergence in one space dimension is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400258
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  • 9
    Electronic Resource
    Electronic Resource
    A three-dimensional quadratic nonconforming element (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 269-279 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We define a second-degree nonconforming element on tetrahedra. We build a basis for the opproximation space derived from this element. We prove a discrete regularity property similar to the one that holds for the corresponding two-dimensional element.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390424
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  • 10
    Electronic Resource
    Electronic Resource
    Monotone iterative methods for finite difference system of reaction-diffusion equations (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 571-586 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper presents an existence-comparison theorem and an iterative method for a nonlinear finite difference system which corresponds to a class of semilinear parabolic and elliptic boundary-value problems. The basic idea of the iterative method for the computation of numerical solutions is the monotone approach which involves the notion of upper and lower solutions and the construction of monotone sequences from a suitable linear discrete system. Using upper and lower solutions as two distinct initial iterations, two monotone sequences from a suitable linear system are constructed. It is shown that these two sequences converge monotonically from above and below, respectively, to a unique solution of the nonlinear discrete equations. This formulation leads to a well-posed problem for the nonlinear discrete system. Applications are given to several models arising from physical, chemical and biological systems. Numerical results are given to some of these models including a discussion on the rate of convergence of the monotone sequences.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389659
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  • 11
    Electronic Resource
    Electronic Resource
    L 2 estimates for the finite element method for the Dirichlet problem with singular data (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 627-632 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we consider the approximation by the finite element method of second order elliptic problems on convex domains and homogeneous Dirichlet condition on the boundary. In these problems the data are Borel measures. Using a quasiuniform mesh of finite elements and polynomials of degree ≦1, we prove that in two dimensions the convergence is of orderh inL 2 and in three dimensions of orderh 1/2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389461
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  • 12
    Electronic Resource
    Electronic Resource
    Numerical solution of a hyperbolic free boundary problem with a method of characteristics (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 85-99 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N99 ; 35R35 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For a free boundary problem for a linear hyperbolic system in one space dimension with two unknowns we discuss a numerical algorithm which combines the method of characteristics and the front tracking method. We prove quadratic resp. linear convergence and illustrate this with numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400257
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  • 13
    Electronic Resource
    Electronic Resource
    On finite element methods for the Neumann problem (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 587-598 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The Neumann problem for a second order elliptic equation with self-adjoint operator is considered, the unique solution of which is determined from projection onto unity. Two variational formulations of this problem are studied, which have a unique solution in the whole space. Discretization is done via the finite element method based on the Ritz process, and it is proved that the discrete solutions converge to one of the solutions of the continuous problem. Comparison of the two methods is done.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389660
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  • 14
    Electronic Resource
    Electronic Resource
    Alternating iteration and elliptic variational inequalities (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 459-481 
    Details
    ISSN: 0945-3245
    Keywords: MR 35A40 ; MR 39-04 ; MR 65N05 ; MR 65N20 ; MR 36S05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Free boundary value problems, too complicated for formulation as a variational inequality, are broken up into two problems on overlapping regions. On one region the problem is treated as an ordinary boundary value problem; on the second region, the “free boundary part” of the problem is reduced to a variational inequality. By solving the two problems successively it is shown that under certain conditions the successive solutions converge to a single function that gives a solution of the original problem. Application to a filtration problem is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389592
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