On convergence of nonconforming convex quadrilateral finite elements AGQ6

The 4-node quadrilateral membrane elements AGQ6-I and II are two novel incompatible models formulated by the Quadrilateral Area Coordinate Method (QACM). In this paper, the sufficient conditions for their convergence are established. It is further shown theoretically that the convergence in the energy norm is linear, and the convergence in the L2 norm is quadratic provided that certain geometric conditions are met requiring asymptotically parallelograms meshes to be used. The necessity of conditions is also discussed. The results of numerical examples completely confirm the theoretical findings.