Abstract
This paper is the third of a series in which a general theory of a priori error estimates for scalar conservation laws is constructed. In this paper, we consider multidimensional flux-splitting monotone schemes denned on non-Cartesian grids. We identify those schemes which are consistent and prove that the L∞ (0, T; L1 (ℝd))-norm of the error goes to zero as (Δx)1/2 when the discretization parameter δx goes to zero. Moreover, we show that nonconsistent schemes can converge at optimal rates of (Δx)1/2 because (i) the conservation form of the schemes and (ii) the so-called consistency of the numerical fluxes allow the regularity properties of the approximate solution to compensate for their lack of consistency.
Original language | English (US) |
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Pages (from-to) | 1775-1803 |
Number of pages | 29 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 35 |
Issue number | 5 |
DOIs | |
State | Published - 1998 |
Keywords
- A priori error estimates
- Conservation laws
- Irregular grids
- Monotone schemes
- Supraconvergence