Abstract:

A Hermite-type rectangular finite element approximation is discussed for nonlinear hyperbolic equation. The superclose property in H1-norm is obtained by use of high accuracy analysis of the element, meanvalue theorem and the derivative transfering technique. The superconvergence result is derived with interpolation postprocessing method. Finally, the fourthorder extrapolation estimation which is as same as that of the linear problem is deduced through constructing a new extrapolation scheme.

Key words: nonlinear hyperbolic equation; superclose and superconvergence; Hermite-type rectangular element; extrapolation