A general adaptive grid algorithm is developed on triangular grids. The adaptivity is provided by a combination of node addition, dynamic node connectivity and a simple node movement strategy. While the local restructuring process and the node addition mechanism take place in the physical plane, the nodes are displaced on a monitor surface, constructed from the salient features of the physical problem. An approximation to mean curvature detects changes in the direction of the monitor surface, and provides the pulling force on the nodes. Solutions to the axisymmetric Grad-Shafranov equation demonstrate the capturing, by triangles, of the plasma-vacuum interface in a free-boundary equilibrium configuration.