Two-Grid method for Characteristic mixed Finite Element Approximations of Nonlinear Convection Diffusion Problems

摘要

A two-grid method for numerically solving nonlinear convection-dominated diffusion problems is presented by using a combination of the method of characteristic with the mixed finite-element. In this approach, the full nonlinear system is solved on a coarse grid of size H. The nonlinearities are expanded about the coarse grid solutions and the resulting linear system is solved on a fine grid of size h. This new method provides the ability to obtain approximations of the solutions and its gradients simultaneously and can solve the nonlinear convection-dominated diffusion problems efficiently. Convergence analysis and error estimates are also established.