Abstract: It is shown that the semi-Lagrangian schemes with cubic spline interpolation are equivalent to a particle-in-cell finite element method. The method conserves mass, is unconditionally stable, and has a truncation error as ...

Abstract: A method to convert conventional semi-Lagrangian schemes into quasi-monotone schemes is given. Numerical examples with linear and nonlinear transport equations demonstrate the ability of our modified semi-Lagrangian schemes ...

Abstract: A conservative quasi-monotone semi-Lagrangian scheme is developed in this paper. Mass conservation is achieved via Lagrange multipliers. The new scheme is computationally efficient. Numerical examples with linear and ...