ANALYSIS OF AN ALGORITHM FOR THE GALERKIN-CHARACTERISTIC METHOD

It is shown that the interpretation of the Galerkin-Characteristic method for the scalar advection equation in the framework of particle methods yields a computationally efficient algorithm. Such an algorithm consists of updating the dependent variable at the grid points by cubic spline interpolation at the feet of the characteristic curves. The algorithm is unconditionally stable. The error analysis in the maximum norm shows that for sufficiently smooth functions the feet of the characteristic curves are points of high order convergence.