an:06176100
Zbl 1273.65121
Heumann, Holger; Hiptmair, Ralf
Convergence of lowest-order semi-Lagrangian schemes
EN
Found. Comput. Math. 13, No. 2, 187-220 (2013).
00317303
2013
j
65M12 65M25 65M60 62M20 35K20
convergence; advection-diffusion problem; discrete differential forms; semi-Lagrangian methods; error estimate
The authors consider a non-stationary advection-diffusion problem for time-dependent differential forms. By means of the Hille-Yosida theorem, the existence and the uniqueness of the transient advection-diffusion problem are obtained. The semi-Lagrangian Galerkin time-stepping scheme for the considered advection-diffusion problem is presented. Under some additional assumptions, an \(L^2\)-estimate of order \(O(\tau+h^r+h^{r+1}\tau^{-1/2}+\tau^{1/2})\) is established, with \(h\) the spatial meshsize, \(\tau\) the time step and \(r\) the polynomial degree of the trial functions.
Ruxandra Stavre (Bucure??ti)