Stability of mixed overlapping elements in incompressible analysis

In this study, we integrated a recently presented pure displacement-based overlapping element with a displacement–pressure mixed formulation. We focused on the idea that the overlapping element that adopts low-order triangles can be effectively integrated with the displacement–pressure mixed formulation without violating the stability condition owing to its enlarged displacement function spaces. By performing numerical stability tests, we obtained the stable displacement–pressure combinations available for practical use. In addition, we demonstrated the effectiveness of the mixed overlapping elements compared with traditional mixed finite elements through numerical examples. Our results imply that the salient feature of the original overlapping element is maintained in incompressible analysis, such that the element is insensitive to mesh distortion and accurate compared to traditional mixed finite elements.