Operator-splitting local discontinuous Galerkin method for multi-dimensional linear convection-diffusion equations

We construct and analyze a local discontinuous Galerkin (LDG) method which is combined with the locally one-dimensional method as one of the splitting methods. The proposed method reduces the size of algebraic system of equations due to the splitting technique, as a result computational time is also reduced. We are particularly interested in improving the computational efficiency in comparison to the original schemes, aiming to preserve the properties of the LDG method. We also deal with the method’s stability and convergence analyses and discuss its computational time. Finally, some numerical simulations are carried out to confirm the theoretical results.