A non-oscillatory DST scheme for solving linear scalar conservation laws

We show the construction and analysis of non-oscillatory direct space-time (DST) discretizations schemes for approximation of linear scaler conservation laws. We develop a nonoscillatory scheme by designing an appropriate limiting function on the flux function. We implement this procedure on the optimal order DST scheme. The resulting scheme has formal high order accuracy and near the discontinuities it the solution is sharp and non-oscillatory. We justify the new scheme with a numerical test based on advection equation and demonstrate the accuracy of the solution and the mentioned non-oscillatory behavior.