A-priori Domain Decomposition of PDE Systems and Applications

Domain Decomposition has been extensively studied as a tool for parallel computing. But in many cases the problem posed includes domain decomposition in its statement. For these the necessary numerical analysis is different because domain decomposition is not only at the discrete level but also on the continuous problem. Therefore non-matching grids for their numerical solutions is more natural, but requires new error estimates.Our main purpose is to compute with the data of Virtual Reality. In this paper we shall review earlier works, including our own[9][10][11] and we shall present the project freefem3d.