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The sharpness of Kuznetsov’s \(O(\sqrt {\Delta x})\) \(L^ 1\)-error estimate for monotone difference schemes. (English) Zbl 0845.65053
The linear advection equation \[ {\partial u \over \partial t} + a {\partial u \over \partial x} = 0, \quad a = \text{const}; \quad u(x,0) = u_0 (x) \] is approximated by a conservative monotone difference scheme. The authors formulate and prove a theorem, that the lower \(L^1\)-error bound for this kind of difference method is \(O (\sqrt {\Delta x})\), where \(\Delta x\) is the spatial stepsize.
Reviewer: M.Fritsche (Jena)

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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