The numerical solution of linear elliptic partial differential equations most often involves a
finite element or finite difference discretization. To preserve sparsity, the arising system is
normally solved using an iterative solution method, commonly a preconditioned conjugate
gradient method. Preconditioning is a crucial part of such a solution process. In order to
enable the solution of very large-scale systems, it is desirable that the total computational
cost will be of optimal order, ie proportional to the degrees of freedom of the approximation …

The numerical solution of linear elliptic partial differential equations often involves finite
element discretization, where the discretized system is usually solved by some conjugate
gradient method. The crucial point in the solution of the obtained discretized system is a
reliable preconditioning, that is to keep the condition number of the systems under control,
no matter how the mesh parameter is chosen. The PCG method is applied to solving
convection–diffusion equations with nonhomogeneous mixed boundary conditions. Using …