Preconditioning by Gram matrix approximation for diffusion–convection–reaction equations with discontinuous coefficients Original Research Article

This work analyses the preconditioning with Gram matrix approximation for the numerical solution of a linear convection–diffusion–reaction equation with discontinuous diffusion and reaction coefficients. The standard finite element method with piecewise linear test and trial functions on uniform meshes discretizes the equation. Three preconditioned conjugate gradient algorithms solve the discrete linear system: CGS, CGSTAB and GMRES. The preconditioning with Gram matrix approximation consists of replacing the solving of the equation with the preconditioner by two symmetric MG iterations. Numerical results are presented to assess the convergence behaviour of the preconditioning and to compare it with other preconditioners of multilevel type.