Cloth animation is a very expensive process in terms of computational cost, due to the flexible nature of cloth objects. Since wrinkles and smooth areas co-exist commonly in cloth, it is tempting to reduce computational cost by avoiding redundant tessellation at the smooth areas. In this paper we present a method for dynamic adaptation of triangular meshes suitable for cloth simulation. A bottom-up approach is used for mesh refinement, which does not require precomputation and storage of multiresolution hierarchy. The hierarchy is constructed in runtime and allows reverting of the refinement locally. Local mesh refinement and simplification are triggered by curvature-induced criterion, where the curvature is estimated using methods of discrete differential geometry. The results presented are the realistic animation of garment worn by a walking mannequin generated with Baraff-Witkin type cloth solver enhanced with the mesh adaptation scheme.