Efficient Solver for Convection-Diffusion Equations

Title of Dissertation: On the Implementation of an Accurate and Efficient Solver for Convection-Diffusion Equations Chin-Tien Wu, Doctor of Philosophy, Nov 2003 Dissertation directed by: Dr. Howard C. Elman Department of Computer Science In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addiiton, both methods are also used as