Overlapping finite element meshes in AMORE

The AMORE scheme of "automatic meshing with overlapping and regular elements" has been recently proposed, in which the concept of overlapping finite elements plays a central role. In earlier work we focused on the overlapping of individual elements. In this paper, we present a technique to overlap finite element meshes so that elements from different meshes can overlap in any geometric form. Meshes for different parts of the analysis domain can be independently spanned, which is an effective way to adapt meshes to various geometric features and solution gradients. Hence, the meshing effort is much reduced and high solution accuracy is achieved. We formulate the new scheme, analyze its solvability and convergence, and propose an implementation. The solutions of some engineering problems are given to illustrate the use and performance of the new scheme.