Rank deficiency in superconvergent patch recovery techniques with 4-node quadrilateral elements

The linear systems of equations generated by the Superconvergent Patch Recovery technique (Int. J. Numer. Methods Eng. 1992; 33:1331–1382; Comput. Methods Appl. Mech. Eng. 1992; 101:207–224) can exhibit rank deficiency under certain purely geometric conditions. The rank deficiency problem can be corrected simply and efficiently by utilizing a local rotated co-ordinate system. This rotated SPR procedure is easily automated and adds robustness to automatic adaptive solution methods. Copyright © 2006 John Wiley & Sons, Ltd.