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  • Engineering General  (43)
  • 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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  • 2
    Electronic Resource
    Electronic Resource
    Performance of iterative methods for Newtonian and generalized Newtonian flows (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 127-150 
    Details
    ISSN: 0271-2091
    Keywords: Iterative solution ; Viscous flow ; Generalized conjugate gradient ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We consider the use of accelerated gradient-type iterative methods for solution of Newtonian and certain non-Newtonian (power-law and Bingham models) viscous flow problems. The formulations are based on penalty and mixed finite element methods, and such factors as the effect of the penalty parameter, asymmetry, continuation and preconditioning are examined.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090202
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  • 3
    Electronic Resource
    Electronic Resource
    On the computed pressures for Navier-Stokes problems at increasing Reynolds numbers using the penalty finite element method (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 439-442 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650050504
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  • 4
    Electronic Resource
    Electronic Resource
    Local pressure oscillation and boundary treatment for the 8-node quadrilateral (1986)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 165-172 
    Details
    ISSN: 0271-2091
    Keywords: Pressure Oscillations ; Driven Cavity ; Boundary Data ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The 8-node (serendipity) velocity basis with C° bilinear pressure is a popular element but has been observed to yield poor pressures. We present some details of numerical experiments that indicate the local nature of the error and the effects of mesh refinement, increasing Reynolds number and regularity of the data. This leads to a strategy for appropriately modifying the data near the corners that is effective in improving the computed pressure approximation.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650060306
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  • 5
    Electronic Resource
    Electronic Resource
    Turbulent boundary-layer analysis using finite elements (1986)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 769-787 
    Details
    ISSN: 0271-2091
    Keywords: Turbulent Boundary Layer ; Kκ-ε Model ; Dorodnitsyn Finite Element ; Heat Transfer ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The use of finite element methods for turbulent boundary-layer flow is relatively recent and of limited extent.1 In the present study, we extend the group variable approach of Fletcher and Fleer2,3 to treat turbulent boundary layer flows with heat transfer using a two-equation turbulence model. The main concepts in the formulations include a Dorodnitsyn-type transformation which uses a velocity component as the transverse variable, a ‘variational’ formulation for the transformed equations using special test functions and development of a two-equation turbulence model in terms of the turbulent kinetic energy and turbulence dissipation rate as additional field variables. Several numerical test cases have been examined comparing the results with finite difference calculations and comparing the two-equation turbulence model with an algebraic turbulence model.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650061102
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  • 6
    Electronic Resource
    Electronic Resource
    Stream function solution of Navier-Stokes problems with inter-element penalties (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 191-193 
    Details
    ISSN: 0271-2091
    Keywords: Finite Elements ; Interface Penalties ; Viscous Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this note, we apply a finite element stream function formulation with inter-element penalties to the Navier-Stokes equations. The approach is an extension of a technique previously introduced for Stokes, flow. The solution is obtained by iterative linearization using successive approximation, and results for a standard numerical test case are given.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070207
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  • 7
    Electronic Resource
    Electronic Resource
    Least-squares finite element methods for compressible Euler equations (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 557-568 
    Details
    ISSN: 0271-2091
    Keywords: Compressible Euler equations ; Finite element ; Least-squares method ; Shock resolution ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L2-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L2-method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100504
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  • 8
    Electronic Resource
    Electronic Resource
    FINITE ELEMENT ANALYSIS OF ANISOTROPIC FLUID SUSPENSIONS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 11-27 
    Details
    ISSN: 0271-2091
    Keywords: finite elements ; liquid crystal ; nematic ; anisotropic ; electro rheological ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The orientation tensor L is introduced to construct a modified Leslie-Ericksen model for the viscous, incompressible flow of anisotropic suspensions (including electric field effects). This is then utilized to develop a weak variational formulation and finite element scheme for computing the flow and orientation fields. Numerical results are presented for exploratory test problems.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Lifting aerofoil calculation using the boundary element method (1983)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 481-491 
    Details
    ISSN: 0271-2091
    Keywords: Boundary Elements ; Lifting Aerofoil ; Potential Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The bbundary integral formulation and boundary element method are extended to include lifting flow problems. This involves inclusion of a branch cut in the flow field and imposition of a Kutta condition to determine the circulation, Γ Additional boundary integral contributions arise from the cut surface. Techniques for calculating Γ are developed and we treat, in particular, a superposition procedure which permits very efficient computation. Numerical results are presented for an NACA0012 aerofoil at several angles of attack.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650030504
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  • 10
    Electronic Resource
    Electronic Resource
    Coupled heat transfer and viscous flow, and magnetic effects in weld pool analysis (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 713-730 
    Details
    ISSN: 0271-2091
    Keywords: Viscous flow ; Heat transfer ; Phase change ; Finite elements ; Magnetic field ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element formulation and analysis is developed to study coupled heat transfer and viscous flow in a weld pool. The thermal effects generate not only buoyancy forces but also a variation in the surface tension which acts to drive the viscous flow in the molten weld pool. A moving phase boundary separates molten and solid material. Numerical experiments reveal the nature of the highly convective flow in the weld pool and the associated thermal profiles. The relative importance of buoyancy, surface tension, phase change, convection, etc. are examined. We also consider the sensitivity of the solution to the finite element mesh and related non-linear numerical instabilities. Of particular interest is the coupling of the thermal and viscous flow fields for the case when radial flow is inward or outward.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090605
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