The characteristic finite element alternating direction method with moving meshes for nonlinear convection-dominated diffusion problems

In modern numerical simulation of prospecting and exploiting oil-gas resources and in environmental science, it is necessary to consider numerical method of nonlinear convection-dominated diffusion problems. This thesis, starting from actual conditions such as the three-dimensional characteristics of large-scale science-engineering computation, puts forward a kind of characteristic finite element alternating direction method with moving meshes. Some techniques, such as calculus of variations, operator-splitting, generalized L-2 projection, energy method, negative norm estimate, the theory of prior estimates and techniques, are adopted. Optimal order estimates in L-2 norm are derived to determine the errors in the approximate solution. Thus the important theoretical problem has been solved. (C) 2005 Wiley Periodicals, Inc.