Abstract: A numerical method is presented for the variable coefficient, nonlinear advection equation $u_t + \sum_{i=1}^d V_i(x,t) f_i(u)_{x_i} = 0$ in arbitrary space dimension for bounded velocities that are Lipschitz continuous in the $x$ variable. The method is based on dimensional splitting and uses a recent front tracking method to solve the resulting one-dimensional non-conservative equations. The method is unconditionally stable, and it produces a subsequence that converges to the entropy solution as the discretization of time and space tends to zero. Three numerical examples are presented.
mailto:conservation@math.ntnu.no Last modified: Tue Nov 18 10:00:13 1997