On Accuracy of Lax-Friedrichs Scheme for Discontinuous Solutions of Convection Equations

Derive L-2-error bounds for Lax-Friedrichs schemes for discontinuous solutions oflinear hyperbolic convection equations.It is known that the Lax-Friedrichs scheme is a firstorder scheme.Analyzes convergent rate of the scheme through its modified equations andshows that the first order Lax-Friedrichs scheme to approach BV solutions of the convectionequation has L￣2-error bounds of O(△x￣(1/4)),where △x is the discrete mesh length.Nemericalexperiments are presented and numerical results justify the theoretical analysis.