Refinement strategies in adaptive meshing

Two strategies for reducing the overall number of finite-element computations needed in an adaptive meshing algorithm are proposed. In the first strategy (called two-threshold refinement), numerical values of the estimated local error are used both to select the elements to be refined and to decide into how may new elements each of them will be subdivided. In the second strategy (called refinement with solution estimation), a solution approximation and its local error on a mesh are estimated from a previous approximation solution. For both methods the required algorithms are presented and the results obtained are compared and discussed. The refinement with solution estimation gives a significant improvement with respect to the usual single threshold refinement method. The two-threshold refinement strategy, even though it has produced errors not always greater than those produced by the single-threshold refinement method, has proven to be worse in general. This result has confirmed the importance of performing Delaunay triangulation each time an element is subdivided