Local defect correction with slanting grids

The local defect correction (LDC) method is used to solve a convection-diffusion-reaction problem that contains a high activity region in a relatively small part of the domain. The improvement of the solution on a coarse grid is obtained by introducing a correction term computed from a local fine grid solution. This paper studies problems where the high activity region is covered with a rectangular fine grid not aligned with the axes of the global domain. This study shows that the resulting method is less expensive than both a uniform refinement and tensor product grid method.