Abstract In this paper, we solve nonlinear conservation laws using the radial basis function generated finite difference (RBF-FD) method. Nonlinear have solutions that entail strong discontinuities and shocks, which give rise to numerical instabilities when solution is approximated by a We introduce residual-based artificial viscosity (RV) stabilization framework adjusted RBF-FD method, where r...

In this work we consider a convolution model for nonlinear conservation laws. Due to the delicate balance between the nonlinear convection and the nonlocal forcing, this model allows for narrower shock layers than those in the viscous Burgers’ equation and yet exhibits the conditional finite time breakdown as in the damped Burgers’ equation. We show the critical threshold phenomenon by presenti...

We analyze the convergence of the overlapping Schwarz waveform relaxation algorithm applied to convection-dominated nonlinear conservation laws in one spatial dimension. For two subdomains and bounded time intervals we prove superlinear asymptotic convergence of the algorithm in the parabolic case and convergence in a finite number of steps in the hyperbolic limit. The convergence results depen...