Superconvergent derivative recovery for the intermediate finite element family of the second type (Q2748864)

This paper deals with the Dirichlet problem NEWLINE\[NEWLINE-\Delta u+ bu= f\quad\text{in }\Omega,\quad u|_{\partial\Omega}= 0,NEWLINE\]NEWLINE \(b\geq 0\), \(b\) and \(f\) are sufficiently smooth such that the solution \(u\) has the required regularity, \(\Omega\) a polygonal domain that can be decomposed into rectangles with sides parallel to the coordinate axes. A recovery technique that provides a superconvergence of order two on the whole domain or a subdomain is presented. The authors bring a purely theoretical matter into a practically feasible recovery technique. Theoretical results are supported by numerical tests.