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A nonstandard finite element method for initial-boundary value problems for first-order hyperbolic systems in one space dimension with general boundary conditions is analyzed. The method can be considered as a generalization of the box scheme. We first establish a stability result for the method and then derive several error estimates.doi:10.1090/s0025-5718-1981-0595042-6 fatcat:ghcaxpl2tzepzapahfsji2o6kq