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  • 1
    Electronic Resource
    Electronic Resource
    Analysis of Thorium-Chromium Mixtures (1948)
    s.l. : American Chemical Society
    Analytical chemistry 20 (1948), S. 233-235 
    Details
    ISSN: 1520-6882
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ac60015a012
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  • 2
    Electronic Resource
    Electronic Resource
    Local refinement techniques for elliptic problems on cell-centered grids (1991)
    Springer
    Numerische Mathematik 59 (1991), S. 431-452 
    Details
    ISSN: 0945-3245
    Keywords: 65F10 ; 65N20 ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Algebraic multilevel analogues of the BEPS preconditioner designed for solving discrete elliptic problems on grids with local refinement are formulated, and bounds on their relative condition numbers, with respect to the composite-grid matrix, are derived. TheV-cycle and, more generally,v-foldV-cycle multilevel BEPS preconditioners are presented and studied. It is proved that for 2-D problems theV-cycle multilevel BEPS is almost optimal, whereas thev-foldV-cycle algebraic multilevel BEPS is optimal under a mild restriction on the composite cell-centered grid. For thev-fold multilevel BEPS, the variational relation between the finite difference matrix and the corresponding matrix on the next-coarser level is not necessarily required. Since they are purely algebraically derived, thev-fold (v〉1) multilevel BEPS preconditioners perform without any restrictionson the shape of subregions, unless the refinement is too fast. For theV-cycle BEPS preconditioner (2-D problem), a variational relation between the matrices on two consecutive grids is required, but there is no restriction on the method of refinement on the shape, or on the size of the subdomains.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385790
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  • 3
    Electronic Resource
    Electronic Resource
    Finite difference schemes on grids with local refinement in time and space for parabolic problems I. Derivation, stability, and error analysis (1990)
    Springer
    Computing 45 (1990), S. 193-215 
    Details
    ISSN: 1436-5057
    Keywords: AMS (MOS) ; 65M05 ; 65M10 ; 65M15 ; Finite difference scheme, cell-centered grids ; local refinement ; refinement in time ; error estimates ; parabolic problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden Differenzenverfahren für parabolische Anfangswertprobleme für zellenorientierte räumliche Gitter (rechteckig für zwei Raumdimensionen) mit regulärer lokaler Verfeinerung bzgl. Zeit und Raum vorgestellt. Ihre Stabilitäts- und Konvergenzeigenschaften werden studiert. Die Differenzenverfahren basieren auf der Idee der finiten Volumina durch Approximation der Bilanzgleichungen und erhalten die Masse (bzw. die Energie). Die Approximation an den Gitterpunkten nahe der Überschneidung von feineren und gröberen Gittern verwendet eine frühere Idee der Autoren für selbstadjungierte elliptische Operatoren. Die vorgeschlagenen Verfahren sind implizit vom Typ “Euler rückwärts” und unkonditioniert stabil. Eine Fehleranalyse ist angeschlossen.
    Notes: Abstract Finite difference schemes for parabolic initial value problems on cell-centered grids in space (rectangular for two space dimensions) with regular local refinement in space as in time are derived and their stability and convergence properties are studied. The construction of the finite difference schemes is based on the finite volume approach by approximation of the balance equation. Thus the derived schemes preserve the mass (or the heat). The approximation at the grid points near the fine and coarse grid interface is based on the approach proposed by the authors in a previous paper for selfadjoint elliptic equations. The proposed schemes are implicit of backward Euler type and are shown to be unconditionally stable. Error analysis is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02250633
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  • 4
    Electronic Resource
    Electronic Resource
    Finite Volume Element Approximations of Nonlocal in Time One-Dimensional Flows in Porous Media (2000)
    Springer
    Computing 64 (2000), S. 157-182 
    Details
    ISSN: 1436-5057
    Keywords: AMS Subject Classifications: 65M12, 65M60, 65N40. ; Key Words: Finite volume method, parabolic equation, integro-differential equation.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Various finite volume element schemes for parabolic integro-differential equations in 1-D are derived and studied. These types of equations arise in modeling reactive flows or material with memory effects. Our main goal is to develop a general framework for obtaining finite volume element approximations and to study the error analysis. We consider the lowest-order (linear and L-splines) finite volume elements, although higher-order volume elements can be considered as well under this framework. It is proved that finite volume element approximations are convergent with optimal order in H 1-norms, suboptimal order in the L 2-norm and super-convergent order in a discrete H 1-norm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s006070050007
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  • 5
    Electronic Resource
    Electronic Resource
    Local refinement techniques for elliptic problems on cell-centered grids; II. Optimal order two-grid iterative methods (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 1 (1994), S. 337-368 
    Details
    ISSN: 1070-5325
    Keywords: Local refinement ; Preconditioning ; Two-grid method ; Cell-centered grids ; Finite differences ; Elliptic problem ; Optimal rate of convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two preconditioning techniques for solving difference equations arising in finite difference approximation of elliptic problems on cell-centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher-order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG-LS in the nonsymmetric case) are presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680010403
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  • 6
    Electronic Resource
    Electronic Resource
    Characteristic adaptive subdomain methods for reservoir flow problems (1990)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 6 (1990), S. 279-309 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The simulation of multiphase and multicomponent fluid flows often requires the solution of large, coupled systems of nonlinear partial differential equations of convection-advection type. The equations are usually advection dominated with small but important local diffusive effects. An operator-splitting technique is used to address these different phenomena. A modified method of characteristics is used to try to eliminate the nonsymmetry in the operators due to advection. Although this method does not completely symmetrize the problem with nonlinear, nonconvex flux functions, the remaining operator is almost symmetric and can be stabilized via Petrov-Galerkin techniques with optimal or near optimal test functions. Effective localized test functions are descrbed. A coarse grid is defined to treat the slow variation of the fluid velocity away from fronts. A substructuring of this grid gives a proper frontal resolution via local patch grid refinement. Preconditioning techniques are presented to efficiently solve the resulting composite-grid problem. Error estimates for the total approximation procedure are presented. Finally, certain two-dimensional computations are described.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690060402
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  • 7
    Electronic Resource
    Electronic Resource
    Mixed finite element methods for computing groundwater velocities (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 195-207 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Central to the understanding of problems in water quality and quantity for effective management of water resources is the development of accurate numerical models to stimulate groundwater flows and contaminant transfer. We discuss several important difficulties arising in modeling of subsurface flow and present promising numerical procedures for alleviating these problems. Furthermore, we describe mixed-finite element techniques for accurately approximating fluid velocities, and review computational results on a variety of hydrologic problems.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010304
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  • 8
    Electronic Resource
    Electronic Resource
    Nonlinear instability for a modified form of Burgers' equation (1987)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 3 (1987), S. 51-64 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690030105
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  • 9
    Electronic Resource
    Electronic Resource
    Optimal-order convergence rates for Eulerian-Lagrangian localized adjoint methods for reactive transport and contamination in groundwater (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 1-31 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Eulerian-Langrangian localized adjoint methods (ELLAM) were developed to solve convection-diffusion-reaction equations governing contaminant transport in groundwater flowing through a porous medium, subject to various combinations of boundary conditions. In this article, we prove optimal-order error estimates and some superconvergence results for the ELLAM schemes. In contrast to many existing estimates for a variety of numerical methods, which often contain the temporal derivatives of the exact solution, our error estimates contain the total derivatives of the exact solution but do not involve any temporal derivatives of the exact solution. © 1995 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110103
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  • 10
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    A Galerkin procedure for systems of differential equations (1980)
    Springer
    Details
    Publication Date: 1980-01-01
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
    Published by Springer
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