A two-grid parallel partition of unity finite element scheme (Q1717576)

For linear elliptic boundary value problems a two-grid parallel partition of unity finite element scheme is proposed and analyzed. This interesting scheme features include: \begin{itemize} \item[(1)] a partition of unity is constructed to derive the globally continuous finite element solution; \item[(2)] errors decay exponentially with patches of diameter kH increase; and \item[(3)] a global coarse grid correction is done to improve the \(L2\)-accuracy of the approximation. \end{itemize} Numerical experiments are presented at the end to support our analysis.