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  • AMS Subject Classifications: 65M12, 65M60, 65N40.  (1)
  • Finite differences  (1)
  • 1
    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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  • 2
    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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    Paper (German National Licenses)
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