1994
DOI: 10.1090/psapm/048/1314852
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Finite volume methods for irregular one-dimensional grids

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Cited by 3 publications
(4 citation statements)
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“…In [7], [28] h-box values were defined in a similar way, and the resulting scheme was shown to give good results for advection and Burgers's equation. One time step of the h-box method based on the interpolation formula (3.3) again for a > 0 has in the small cell the form…”
Section: H)mentioning
confidence: 99%
See 1 more Smart Citation
“…In [7], [28] h-box values were defined in a similar way, and the resulting scheme was shown to give good results for advection and Burgers's equation. One time step of the h-box method based on the interpolation formula (3.3) again for a > 0 has in the small cell the form…”
Section: H)mentioning
confidence: 99%
“…An extension of h-box methods to a completely irregular grid was considered by Berger, LeVeque, and Stern [7]; see also Stern [28]. We will consider such calculations in section 5.…”
Section: Introductionmentioning
confidence: 99%
“…Although customary, such a condition might be unreasonably stringent for most of the elements. An interesting alternative is discussed in [1].…”
Section: The Numerical Schemes and The Main Resultsmentioning
confidence: 99%
“…Actually in Wendroff and White [31], [30] and Wendroff [29], a grid function is introduced for suitably smooth solutions of hyperbolic system in order to prove the optimal order of convergence of upwind finite difference and Lax-Wendroff schemes in one dimension space and in two dimension when an Alternate Direction Method is used. Berger et al [4], [3] successfully used the idea to get the optimal rate of convergence of the "h-box" scheme defined on a non-uniform cartesian grid with embedded irregular small cells. Recently Després [9], [8], by using energy estimates, has given an elegant proof of an order h 1/2 error estimates with respect to the L 2 norm for the linear advection equation on regular finite element meshes in the particular case of periodic boundary conditions.…”
mentioning
confidence: 99%