Volumetric locking in natural neighbour Galerkin methods

The behaviour of natural neighbour Galerkin mixed approximation is described at the incompressible limit. Traditional natural elements based on the Sibson mixed interpolation do not verify the LBB (or inf–sup) condition. Here, a study of the possible benefits of enriching the interpolation is considered using the partition of unity paradigm. Different enrichments were tested leading to different reproducing properties. Results concerning the numerical verification of the inf–sup tests are addressed. Also the convenience of using different approximations developed in this work is analysed. Enrichment with the polynomial field {1, xy} seems to verify the LBB condition. Its behaviour has proven to be very similar to the MINI Finite Element, widely used in the literature. Examples proving these results are provided