Interpolation error estimates of a modified 8-node serendipity finite element

Interpolation error estimates for a modified 8-node serendipity finite element are derived in both regular and degenerate cases, the latter of which includes the case when the element is of triangular shape. For u is an element of W-3,W-p (K) defined over a quadrilateral K, the error for the interpolant Pi(K)u is estimated as \u - Pi(K)u\(W)alpha,p((K)) less than or equal to Ch(K)(3-alpha)\u\(W)3,p((K)) (alpha = 0, 1), where 1 less than or equal to p less than or equal to +infinity in the regular case and 1 less than or equal to p < 3 in the degenerate case, respectively. Thus, the obtained error estimate in the degenerate case is of the same quality as in the regular case at least for 1 less than or equal to p < 3. Results for some related elements are also given.