Abstract: A posteriori error estimates of residual type for generalized difference method (finite volume method) are derived for 2-D nonlinear parabolic equation on triangular meshes and an adaptive scheme suitable to problems with sharp moving fronts is designed.A data structure (not a tree structure) and a flexible local coarsening method for triangular meshes suitable to adaptive computations for evolution problems are also presented.

Key words: nonlinear parabolic equation, generalized difference method, finite volume method, adaptive computation, coarsening method for triangular meshes