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  • 1
    Digitale Medien
    Digitale Medien
    Mixed finite element methods for a dynamical Ginzburg-Landau model in superconductivity (1997)
    Springer
    Numerische Mathematik 76 (1997), S. 323-353 
    Details
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991):65N30, 82D55
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. In this paper we consider the numerical solutions of the nonlinear time-dependent Ginzburg-Landau model which describes the phase transitions taking place in superconducting films. We propose a semi-implicit finite element scheme which is based on a linear finite element approximation of the order parameter $\psi$ and a mixed finite element discretization for the equation involving the magnetic potential A. The error estimates of the scheme are derived.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002110050266
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  • 2
    Digitale Medien
    Digitale Medien
    Finite element methods and their convergence for elliptic and parabolic interface problems (1998)
    Springer
    Numerische Mathematik 79 (1998), S. 175-202 
    Details
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991):65N30, 65F10
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract. In this paper, we consider the finite element methods for solving second order elliptic and parabolic interface problems in two-dimensional convex polygonal domains. Nearly the same optimal $L^2$ -norm and energy-norm error estimates as for regular problems are obtained when the interfaces are of arbitrary shape but are smooth, though the regularities of the solutions are low on the whole domain. The assumptions on the finite element triangulation are reasonable and practical.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002110050336
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  • 3
    Digitale Medien
    Digitale Medien
    Residual type a posteriori error estimates for elliptic obstacle problems (2000)
    Springer
    Numerische Mathematik 84 (2000), S. 527-548 
    Details
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991): 65N15, 65N30; 41A05, 41A29, 41A36
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. A posteriori error estimators of residual type are derived for piecewise linear finite element approximations to elliptic obstacle problems. An instrumental ingredient is a new interpolation operator which requires minimal regularity, exhibits optimal approximation properties and preserves positivity. Both upper and lower bounds are proved and their optimality is explored with several examples. Sharp a priori bounds for the a posteriori estimators are given, and extensions of the results to double obstacle problems are briefly discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002110050009
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  • 4
    Digitale Medien
    Digitale Medien
    On a non-stationary Ginzburg-Landau superconductivity model (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 855-875 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we study a non-stationary superconductivity model derived from Ginzburg-Landau macroscopic theory. By using gauge invariance and studying a linear problem with curl boundary conditions, we obtain the existence of solutions. The solution is unique in the sense of gauge equivalence.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670161203
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