Many graphics applications represent deformable surfaces through dynamic meshes. To be consistent during deformations, the dynamic meshes require an adaptation process. In this paper we present a simple and flexible framework to adapt dynamic meshes following deformable surfaces. Our scheme combines normal and tangential geometric corrections with refinement and simplification resolution control. It works with different surface descriptions, and supports application-specific criteria. We also introduce a stochastic sampling approach to measure the geometric error approximation. As an example, we couple our framework with numerical simulations, such as a particle level-set method. r 2008 Elsevier Ltd. All rights reserved.