THE INTERPOLATION THEOREM FOR NARROW QUADRILATERAL ISOPARAMETRIC FINITE-ELEMENTS

The interpolation theorem for convex quadrilateral isoparametric finit e elements is proved in the case when the condition rho(K)/h(K) greate r than or equal to rho(0) > 0 is not satisfied, where h(K) is the diam eter of the element K and rho(K) is the radius of an inscribed circle in K. The interpolation error is O(h(K)(2)) in the L(2)(K)-norm and O( h(K)) in the H-1(K)-norm provided that the interpolated function belon gs to H-2(K). In the case when the long sides of the quadrilateral K a re parallel the constants appearing in the estimates are evaluated.