With the aid of algebraic methods the discrete solution of a problem is obtained from the discrete problem. At this layer the solution consists of a vector of numbers which has to fulfill the requirements of the given algebraic equation system. When eigenvalue equations are solved, a number of different eigenvalues and the associated eigenvectors are provided. This vector is returned to the discretization layer where the solution vector is considered as weighting vector for basis functions.
If discrete modeling is used, the discrete solution itself becomes relevant. In this special case of a discrete model, which is often used in industrial simulation or electrical circuit simulation, for instance for finding an optimum workload balance for a facility, the model does only contain discretized data and does not have any functional information on distributed quantities.