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  • Numerical Methods  (4)
  • superconvergence  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Convergence analysis of least-squares mixed finite elements (1993)
    Springer
    Computing 51 (1993), S. 111-123 
    Details
    ISSN: 1436-5057
    Keywords: 65N30 ; 65N15 ; 65L10 ; Least-squares ; mixed finite element method ; superconvergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Methode der kleinsten Fehlerquadrate wird bei gemischten finiten Elementen für die Differentialgleichungen erster Ordnung angewandt, die den linearen elliptischen 1-D Randwertaufgaben zweiter Ordnung entsprechen. Es werden theoretische Untersuchungen vorgestellt und Fehlerabschätzungen vorgenommen. Diese sind mit den früther von Carey and Shen [5] veröffentlichten numerischen Analysen konsistent. Die LBB Bedingung ist nicht notwendig und es werden Abschätzungen für verschiedene Grade der Austatz-Polynome vorgenommen. Superkonvergente Abschätzungen werden ebenso vorgestellt.
    Notes: Abstract The least-squares finite element method for first order systems corresponding to second order linear two-point boundary value problems is considered. A theoretical analysis and error estimates are developed and the estimates are seen to be consistent with our previous numerical studies in Carey and Shen [5]. The method is not subject to the LBB condition and we consider, in particular, the estimates when the polynomial degree differs for the corresponding variables. Superconvergence estimates are also developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243846
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Higher-order compact mixed methods (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 553-564 
    Details
    ISSN: 1069-8299
    Keywords: mixed methods ; high-order finite differences ; compact stencils ; superconvergence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We develop a class of higher-order mixed finite difference methods for elliptic partial differential equations. The problem is recast as a first-order mixed system and the higher-order compact schemes follow as a natural extension of the formulations we developed previously for the scalar PDE problem. Since the flux appears explicitly in the mixed formulation we obtain higher-order (nodal superconvergent) solutions in both the primary solution field and also the flux. Some supporting numerical experiments are included to demonstrate the superconvergent rates. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    Natural and postprocessed superconvergence in semilinear problems (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 245-259 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Superconvergence error estimates are established for a class of semilinear problems defined by a linear elliptic operator with a nonlinear forcing term. The analysis is for rectangular biquadratic elements, and we prove superconvergence of the derivative components along associated lines through the Gauss points. Derivative postprocessing formula and formulas for integrals are also considered and similar superconvergence estimates proven.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690070304
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  • 4
    Electronic Resource
    Electronic Resource
    Least-squares finite element approximation of Fisher's reaction-diffusion equation (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 175-186 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Fisher's equation is a classical diffusion-reaction type of problem describing diffusion and nonlinear reproduction of a species. In the present study we develop a least-squares finite element formulation of Fisher's equation and carry out supporting numerical studies. Of particular interest are questions associated with the approximation of progressive wave solutions with minimum speed and the viability of the least-squares approach for this class of problem. © 1995 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110206
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  • 5
    Electronic Resource
    Electronic Resource
    A regularization-stabilization technique for nonlinear conservation equation computations (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 165-171 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A regularization procedure for nonlinear conservation equations is introduced and demonstrated to have a stabilizing effect on the numerical solution of the associated approximate problem. Representative results for a least-squares finite-element method are given, and the numerical performance of the stabilization procedure explored. The effect of the regularization term is similar to a local numerical dissipation dependent on the numerical itegration time step.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690040302
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  • 6
    Electronic Resource
    Electronic Resource
    Superconvergence phenomena in nonlinear two-point boundary-value problems (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 561-577 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Superconvergence estimates are derived for a class of strongly nonlinear two-point boundary-value problems. The analysis considers solution and gradient superconvergence points as well as flux postprocessing formulas. Finally, the extension to parabolic problems is considered. © 1993 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090506
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    Paper (German National Licenses)
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