Local Hierarchical Grid Refinement for Analysis Using Structured Grids

Structured grids with regular shaped uniform elements are easy to generate automatically and have been used in extended finite element approaches to avoid mesh generation difficulties. But the grid or mesh should ideally have higher resolution in areas where the solution has large gradients. In this paper a technique for refinement of structured grids is presented that allows refinement of the grid without violating compatibility requirements by using solution structures constructed using approximate step functions. Essential boundary conditions are applied using implicit boundary method, which allows boundary conditions to be imposed even when there are no nodes on the boundary. This grid refinement technique is evaluated using two dimensional elasticity problems that involve stress concentration.