This paper presents a real-time rendering technique for dynamic, incremental 3D mesh refinement. The technique can be applied to any triangulated 3D mesh with arbitrary topology and connectivity. The functionality relies on geometry shaders that are used to amplify or remove geometry based on precalculated refinement patterns. For each triangle, the instantiated refinement pattern is selected dynamically. Due to limitations of current hardware, on-the-fly pattern instantiation cannot be implemented on the GPU. Instead, the complete refined mesh must be generated through pattern copying. We propose an incremental approach where the refined mesh is generated by using the previous refined mesh as primitive source. This algorithm runs exclusively on the GPU and requires no continuous data exchange between CPU and GPU. Due to the necessary mesh generation, the approach is particularly suitable for applications with small refinement levels. It complements traditional pattern-based refinement approaches that deliver high throughput for large refinement levels, but incur a substantial CPU-GPU communication overhead otherwise. Interesting applications include view-dependent mesh smoothing and interactive non-planar projections. In these areas, our algorithm enables efficient vertex-based implementations due to adaptive refinement.