Solving parabolic problems using local defect correction in combination with the finite volume method

We present a method for solving partial differential equations characterized by highly localized properties in which the local defect correction (LDC) algorithm for time-dependent problems is combined with a finite volume discretization. At each time step, LDC computes a numerical solution on a composite grid, a union of a global uniform coarse grid and a local uniform fine grid. The main feature of the method is that the discrete conservation property, typical of the finite volume approach is preserved on the composite grid