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  • 35J20  (1)
  • two space dimensions  (1)
  • Springer  (2)
  • 1
    Electronic Resource
    Electronic Resource
    A system of conservation laws including a stiff relaxation term; the 2D case (1996)
    Springer
    BIT 36 (1996), S. 786-813 
    Details
    ISSN: 1572-9125
    Keywords: Hyperbolic conservation laws ; two space dimensions ; relaxation terms ; non-equilibrium ; error estimate ; rate of convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We analyze a system of conservation laws in two space dimensions with a stiff relaxation term. A semi-implicit finite difference method approximating the system is studied and an error bound of order $$\mathcal{O}(\sqrt {\Delta t} )$$ measured inL 1 is derived. This error bound is independent of the relaxation time δ 〉 0. Furthermore, it is proved that the solutions of the system converge towards the solution of an equilibrium model as the relaxation time δ tends to zero, and that the rate of convergence measured inL 1 is of order $$\mathcal{O}(\delta ^{1/3} )$$ . Finally, we present some numerical illustrations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01733792
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An upscaling method for one‐phase flow in heterogeneous reservoirs. A weighted output least squares (WOLS) approach (1998)
    Springer
    Computational geosciences 2 (1998), S. 93-123 
    Details
    ISSN: 1573-1499
    Keywords: reservoir simulation ; second order elliptic equations ; upscaling ; homogenization ; 35J25 ; 35J20 ; 73B27
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Computer Science
    Notes: Abstract In this paper we study the problem of determining the effective permeability on a coarse scale level of problems with strongly varying and discontinuous coefficients defined on a fine scale. The upscaled permeability is defined as the solution of an optimization problem, where the difference between the fine scale and the coarse scale velocity field is minimized. We show that it is not necessary to solve the fine scale pressure equation in order to minimize the associated cost‐functional. Furthermore, we derive a simple technique for computing the derivatives of the cost‐functional needed in the fix‐point iteration used to compute the optimal permeability on the coarse mesh. Finally, the method is illustrated by several analytical examples and numerical experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011541917701
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    Paper (German National Licenses)
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