| 1. |
- Dorobantu, M, et al.
(författare)
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Wavelet-based numerical homogenization
- 1998
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Ingår i: SIAM Journal on Numerical Analysis. - 0036-1429 .- 1095-7170. ; 35:2, s. 540-559
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Tidskriftsartikel (refereegranskat)abstract
- A numerical homogenization procedure for elliptic differential equations is presented. It is based on wavelet decompositions of discrete operators in find and coarse scale components followed by the elemination of the fine scale contributions. If the operator is in divergence form, this is preserved by the homogenization procedure. For periodic problems, results similar to classical effective coefficient theory is proved. The procedure can be applied to problems that are not cell-periodic.
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| 2. |
- Efraimsson, Gunilla
(författare)
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A Remark on Numerical Errors Downstream of Slightly Viscous Shocks
- 1999
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1429 .- 1095-7170. ; 36:3, s. 853-863
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Tidskriftsartikel (refereegranskat)abstract
- Lower-order errors downstream of a shock layer have been detected in computations with nonconstant solutions when using higher-order shock capturing schemes in one and two dimensions [B. Engquist and B. Sjögreen, {SIAM J. Numer. Anal., 35 (1998), pp. 2464--2485].By analyzing the steady-state solution of slightly viscous hyperbolic systems of conservation laws we find that the solution can have an ${\cal O}(h)$-dependence downstream of a shock layer, although the viscous term in that region is of ${\cal O}(h^2)$. Numerical examples illustrate the analysis.
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| 3. |
- Engquist, Björn, et al.
(författare)
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Convergence of a multigrid method for elliptic equations with highly oscillatory coefficients
- 1997
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Ingår i: SIAM Journal on Numerical Analysis. - : SIAM Publications. - 0036-1429 .- 1095-7170. ; 34:6, s. 2254-2273
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Tidskriftsartikel (refereegranskat)abstract
- Standard multigrid methods are not so effective for equations with highly oscillatory coefficients. New coarse grid operators based on homogenized operators are introduced to restore the fast convergence rate of multigrid methods. Finite difference approximations are used for the discretization of the equations. Convergence analysis is based on the homogenization theory. Proofs are given for a two-level multigrid method with the homogenized coarse grid operator for two classes of two-dimensional elliptic equations with Dirichlet boundary conditions.
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| 4. |
- Engquist, Björn, et al.
(författare)
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The convergence rate of finite difference schemes in the presence of shocks
- 1998
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Ingår i: SIAM Journal on Numerical Analysis. - 0036-1429 .- 1095-7170. ; 35:6, s. 2464-2485
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Tidskriftsartikel (refereegranskat)abstract
- : Finite difference approximations generically have O(1) pointwise errors close to a shock. We show that this local error may effect the smooth part of the solution such that only first order is achieved even for formally higher-order methods. Analytic and numerical examples of this form of accuracy are given. We also show that a converging method will have the formal order of accuracy in domains where no characteristics have passed through a shock.
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| 5. |
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| 6. |
- Gustafsson, Bertil, et al.
(författare)
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Navier-Stokes equations for almost incompressible flow
- 1991
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 28, s. 1523-1547
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Tidskriftsartikel (refereegranskat)
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| 7. |
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| 8. |
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| 9. |
- Waldén, Johan
(författare)
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Filter bank methods for hyperbolic PDEs
- 1999
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Ingår i: SIAM Journal on Numerical Analysis. - 0036-1429 .- 1095-7170. ; 36, s. 1183-1233
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Tidskriftsartikel (refereegranskat)
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