Implementation and solution of the diffusionreaction equation using high-order methods
The orthogonal collocation, Galerkin, tau and least-squares methods are applied to solve a diffusionreaction problem. In general, the least-squares method suffers from lower accuracy than the other weighted residual methods. The least-squares method holds the most complex linear algebra theory and is thus associated with the most complex implementation. On the other hand, an advantage of the least-squares method is that it always produces a symmetric and positive definite system matrix which can be solved with an efficient iterative technique such as the conjugate gradient method or its preconditioned version. For the present problem, neither the Galerkin, tau and orthogonal collocation techniques produce symmetric and positive definite system matrices, hence the conjugate gradient method is not applicable for these numerical techniques.
least-squares weighted residual methods conjugate gradient catalyst pellet element-by-element technique numerical methods