Abstract: We analyze approximation and propose a two-level algorithm for finite volume schemes of diffusion equations with structured adaptive mesh refinement. First of all, a typically conservative finite volume scheme was discussed, along with criterion for refining and coarsening interpolation operator. Secondly, non-conforming elements around coarse-fine interface were eliminated by introducing auxiliary triangle elements. A symmetric finite volume element (SFVE) scheme was designed. And further analysis showed the scheme has better approximation. It weakens restrictions. Finally, a two-level algorithm was constructed for SFVE. Theoretical analysis and numerical experiments demonstrate uniform convergence of the algorithm.

Key words: adaptive mesh refinement (AMR), diffusion equations, finite volume schemes, approximation, two-level algorithm