Generalized nodes and high-performance elements

The paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition-of-unity-based finite-element approximation. Construction of the partition-of-unity-based approximation is accomplished by a physically defined local function of displacements. A 4-node quadratic tetrahedral element and a 3-node quadratic triangular element are developed. Eigenvalue analysis shows that linear dependencies in the partition-of-unity-based finite-element approximation constructed for the new elements are eliminable. Numerical calculations demonstrate that the new elements are robust, insensitive to mesh distortion, and offer quadratic accuracy, while also keeping mesh generation extremely simple.