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  • 1995-1999  (17)
  • 1990-1994  (17)
  • 1980-1984  (3)
  • 1
    Digitale Medien
    Digitale Medien
    Convergence analysis of least-squares mixed finite elements (1993)
    Springer
    Computing 51 (1993), S. 111-123 
    Details
    ISSN: 1436-5057
    Schlagwort(e): 65N30 ; 65N15 ; 65L10 ; Least-squares ; mixed finite element method ; superconvergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Beschreibung / Inhaltsverzeichnis: 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.
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02243846
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  • 2
    Digitale Medien
    Digitale Medien
    Superconvergence analysis of approximate boundary-flux calculations (1992)
    Springer
    Numerische Mathematik 63 (1992), S. 483-501 
    Details
    ISSN: 0945-3245
    Schlagwort(e): 65N30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Certain projection post-processing techniques have been proposed for computing the boundary flux for two-dimensional problems (e.g., see Carey, et al. [5]). In a series of numerical experiments on elliptic problems they observed that these post-processing formulas for approximate fluxes were almost (O(h 2)-accurate for linear triangular elements. In this paper we prove that the computed boundary flux isO(h 2 ln 1/h)-accurate in the maximum norm for the partial method of [5]. If the solutionuφH 3(Ω) then the boundary flux error isO(h 3/2) in theL 2-norm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01385871
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  • 3
    Digitale Medien
    Digitale Medien
    Galerkin and collocation-Galerkin methods with superconvergence and optimal fluxes (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 939-950 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Finite element methods are formulated and investigated for the effectiveness factor problem for heat and mass transfer with chemical reactions in catalyst pellet models. A Galerkin finite element method is compared with a previous C1 collocation method7. A scheme that is conceptually intermediate between these two methods and accordingly has been termed collocation-Galerkin is formulated and numerical experiments considered. Of particular interest here are superconvergence results at the Gauss and Jacobi points, respectively. Numerical studies of superconvergence in the presence of a nonlinear reaction-rate term are presented. An integral formula is devised and used to compute the flux at the pellet surface to optimal accuracy. Numerical experiments are conducted to demonstrate the improvement in computed fluxes.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620170610
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  • 4
    Digitale Medien
    Digitale Medien
    Variable upwinding and adaptive mesh refinement in convection-diffusion (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 341-353 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: An analysis of the stability and oscillation properties of upwind finite element methods for convection-diffusion is given and used to develop a variable upwinding formulation. This formulation is particularly well suited to problems with nonconstant coefficients, nonlinearity or non-uniform meshes. We present the theoretical analysis and numerical studies for a standard steady-state and transient model one-dimensional convection-diffusion problem. The variable upwind strategy can also be used to significant advantage in conjunction with adaptive mesh refinement. Numerical results for the steady-state case in which convection dominates and the mesh is adaptively refined into a boundary layer confirm the efficacy of the scheme.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620190304
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  • 5
    Digitale Medien
    Digitale Medien
    Moving-grid finite element modelling of thermal ablation and consolidation in porous mediaWork performed in part under the auspices of the U.S. Department of Energy (DOE), Idaho Operations Office, under Contract No. DE-ACO7-76ID01570, the INEL Long Term Research Initiative in Computational Mechanics, the National Science Foundation and the CEOGRR Industrial Associates. (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 717-744 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A moving-grid finite element model for the analysis of thermal ablation, fluid flow and deformation in elastic porous media is presented. The model is formulated in terms of temperatures, fluid pressures and solid displacements, and takes into account a moving phase boundary. Supporting algorithms for treating the moving phase boundary and solving the coupled equations are described. The model has application to several important moving-boundary geotechnical problems. Numerical test cases are provided for model verification and example applications corresponding to thermal ablation, consolidation and underground coal gasification are given.
    Zusätzliches Material: 18 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620360502
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  • 6
    Digitale Medien
    Digitale Medien
    A perturbation analysis and finite element approximate model for free surface flow over curved beds (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 493-507 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A perturbation analysis is developed for 1-D shallow water flow over a curved bed for applications such as spillways. The perturbation approach leads to a new formulation of the problem with associated weak integral statement and approximation using finite elements. The flow may exhibit a hydraulic jump in the downstream regime. An artificial dissipation technique is introduced to stabilize the non-linear problem and suppress numerical oscillations. Numerical results demonstrate the performance of the model and compare it with the steep-slope shallow water formulation corresponding to the model with zero curvature.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620310306
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  • 7
    Digitale Medien
    Digitale Medien
    Shape optimization using adaptive shape refinement (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2435-2451 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A large part of the computational effort in shape optimization problems is expended in the numerical computation of the gradients for sensitivity information. This effort increases dramatically with an increase in the number of variables used to represent the shape. An adaptation of the gradient projection algorithm for shape optimization problems is described here along with a method to reduce the intermediate size of the optimization problem by allowing adaptive refinement of the shape. The method is demonstrated with a simple representative test case.
    Zusätzliches Material: 9 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620361408
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  • 8
    Digitale Medien
    Digitale Medien
    A note on Richardson extrapolation as an error estimator for non-linear reaction-diffusion problems (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 533-540 
    Details
    ISSN: 1069-8299
    Schlagwort(e): extrapolation ; non-linear potential equation ; reaction-diffusion ; semiconductors ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: We develop and test a 6th-order Richardson extrapolation scheme as an error estimator for reaction-diffusion problems. Supporting numerical experiments are presented. © 1997 John Wiley & Sons, Ltd.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    Higher-order compact mixed methods (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 553-564 
    Details
    ISSN: 1069-8299
    Schlagwort(e): mixed methods ; high-order finite differences ; compact stencils ; superconvergence ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: 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.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    Editorial preface for the second decade of Communications in Numerical Methods in Engineering (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. iii 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110102
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