The characteristic finite volume element method for the nonlinear convection-dominated diffusion problem

In modern numerical simulation of prospecting and exploiting oil-gas resources and environmental science, it is important to consider a numerical method for nonlinear convection-dominated diffusion problems. Based on actual conditions, such as the three-dimensional characteristics of large-scale science-engineering computation, we present a kind of characteristic finite volume element method. Some techniques, such as calculus of variations, commutating operators, the theory of prior estimates and techniques, are adopted. Suboptimal order error estimate in L^2 norm and optimal order error estimate in H^1 norm are derived to determine the errors for the approximate solution. Numerical results are presented to verify the performance of the scheme.

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