An iterative perturbation method for saddle point problems

An iterative perturbation method is presented for saddle pointproblems a as an iterative scheme for mixed finite element methods.It can be viewed as an extension of augmented Lagrangian methodsto second-order elliptic equations with a reaction term. Thisiterative method can lead to positive definite systems and decouplethe flux variable from the pressure variable. Convergence analysesare established at the differential and finite-dimensional levels.Various computational experiments for problems with continuousand discontinuous coefficients and full diffusion tensors areconducted to confirm the theoretical claims. These experimentsare implemented in the object oriented programming paradigmusing C++ to take advantage of object oriented software engineeringtechniques such as encapsulation, inheritance, and polymorphism.