Abstract: In this paper, the quadratic and cubic splines local interpolation on a sectorial element in polar coordinates is discussed and a class of spline sectorial elements for analyses of plane and thin problems are presented. A reasonable treatment of the assumed displacement fields for elements with nodes at the origin (r=0) has been made so that the elements can not only characterize the geometrical properties at the origin but also remove the singularity of strains and stresses there. Some numerical examples are given to show the efficiency of the proposed elements.

Key words: magnetohydrodynamic (MHD), chemical reaction, porous medium, viscous dissipation, finite element method