In this paper, we present a meshing scheme for the implementation of an adaptive tessellation of triangular meshes on the graphics processing unit (GPU). Tessellation is performed according to a local test to generate primitives dynamically. The refinement procedure does not require the pre-computation of any refinement pattern. The resulting adaptive procedure is efficient and simple, and generates the tessellation pattern of each triangle dynamically. The non-recursive strategy simplifies mesh reconstruction, avoids irregular memory access patterns and uses a simple control flow to make it a good candidate to guide the evolution of tessellation algorithms on future graphics cards. To test our proposal, we have used the geometry shader of current GPUs to generate primitives dynamically.