Abstract:

A quasi-Wilson finite element method is applied to a class of pseudo-hyperbolic equations. Firstly, employing the known high accuracy analysis of the bilinear element, mean-value approach and post-processing technique, the superclose property and the global superconvergence result with the order O(h2) are obtained for semi-discrete scheme. Secondly, combining a special character of the quasi-Wilson element that the consistency error can reach to order O(h3) in broken H1-norm and extrapolation method, the extrapolation solution with the order O(h3) is presented. Finally, the optimal order error estimate is deduced in broken H1-norm for fully-discrete scheme.

Key words: pseudo-hyperbolic equations; quasi-Wilson element; semi-discrete and fully-discrete schemes; superconvergence and extrapolation; optimal error estimate