On the convergence of overlapping elements and overlapping meshes. (February 2021) - Huang, Junbin; Bathe, Klaus-Jürgen
Highlights: The scheme of "overlapping finite elements" is studied. The scheme of "overlapping meshes" is studied. Convergence properties of the schemes are established. Illustrative examples are presented, including using AMORE. Abstract: Two novel finite element schemes were earlier proposed to reduce the meshing effort needed for practical finite element analysis and their promising performance was demonstrated in the AMORE (AMORE stands for A utomatic M eshing with O verlapping and R egular E lements) framework. In the first scheme "overlapping finite elements" are established that combine advantages of meshless and traditional finite element methods. A key step is to use polynomial interpolations for the rational shape functions in the meshless method. The scheme enables effective, accurate, and element distortion insensitive numerical solutions. In the second scheme, individual meshes are allowed to overlap quite freely. In our earlier papers we gave illustrative examples and also brief discussions on the convergence of the schemes when used in AMORE. We now focus on presenting deeper insights into the convergence properties through theory and novel illustrative solutions.