Dynamic refinement algorithms for spectral element methods Original Research Article

A numerical method is presented that combines high-order domain decomposition and adaptive mesh refinement. The spatial discretization is based on a nonconforming spectral element method. Meshes are generated by adaptive refinement of a quadtree using either local solution gradients or the local polynomial spectrum as a refinement criteria. The method is applied to solve scalar test problems and to simulate the flow in a lid-driven cavity at moderate Reynolds numbers.