Mathematics of Computation · 1995 · 55 citations · 4 references
Natural SciencesMathematicsDifferential EquationsConvergence AnalysisDifference EquationsFinite Difference MethodsNumerical ConvergenceNumerical Methods For Differential EquationsNumerical StabilityAdvectionFinite Difference DiscretizationFinite Difference SchemesMonotone ConvergenceMonotone OperatorsMonotonicity-preserving SchemesStability Of Numerical Schemes
We derive a lower error bound for monotone difference schemes to the solution of the linear advection equation with BV initial data. A rigorous analysis shows that for any monotone difference scheme the lower L 1 -error bound is O(√Δx), where Δx is the spatial stepsize
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