Global superconvergence analysis of Wilson element for Sobolev and viscoelasticity type equations (Q2574285)

The authors consider the following Sobolev type equation \[ \begin{cases} -\Delta u_t-\Delta u=f & \text{ in }\Omega\times(0,T],\\ u=0 & \text{ on }\partial \Omega\times(0,T],\\ u(x,y,0)=V(x,y),\end{cases} \] as well as viscoelasticity type equation \[ \begin{cases} u_{tt}-\Delta u_t-\Delta u=f& \text{ in }\Omega \times(0,T],\\ u=0& \text{ on } \partial\Omega\times(0,T],\\ u(x,y,0)=v(x,y),\;u_t(x,y,0)=\omega(x,y)& \text{ in }\Omega.\end{cases} \] Using the Wilson nonconforming finite element, they solve the above equations. By means of post-processing technique, global superconvergence estimates are obtained on quasi-uniform rectangular meshes. Moreover, the authors present an error correction scheme.