Discontinuous Galerkin FEM of Hybrid Displacement Type<br>—Development of Polygonal Elements—

As a discontinuous Galerkin FEM, we propose a formulation based on Tong’s hybrid displacement method and the stabilization technique, and develop polygonal elements for linear static plane stress problems.The basic ideas are the introduction of inter-element displacements and the use of stabilization terms. Here we only present polygonal elements with polynomial approximation functions.That is, we employ discontinuous linear polynomial fields for element displacements, while we adopt continuous piecewise linear polynomial fields for inter-element displacements. By static condensation, we can also obtain the usual element stiffness matrices and the element load vectors for nodal inter-element edge displacements, so that our elements can be easily built into various existing FEM codes and even mixed use with conventional elements is possible. We obtain some numerical results to show the validity of our approach and also to see the influence of the stabilization parameter size and the flexibility in element shape.