| Abstract: | 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 L2 projection, energy method, negative norm estimate, the theory of prior estimates and techniques, are adopted. Optimal order estimates in L2 norm are derived to determine the errors in the approximate solution. Thus the important theoretical problem has been solved. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 |
