The PCD Method

摘要

We propose in this contribution a new BVP discretization method which represents the unknown distribution as well as its derivatives by piecewise constant distributions (PCD) but on distinct meshes. Once the meshes are chosen, it is relatively straightforward to define an approximate variational formulation of the BVP on the associated PCD spaces and hence to derive the discrete equations. We end with the same scheme as the corner mesh box method and we display a precise relation between the exact solution and our approximation, which holds in the absence of absorption. We also compare these results with other approaches using a mixed variational formulation of the same BVP and sharing with our method the use of several meshes. We show that PCD approximations can also be used in this context leading, on rectangular meshes, to the same scheme as the centered box method.