The optimal point of the gradient of finite element solution (Q1092633)

Consider the following Dirichlet problem: \[ -(au_ x+bu_ y)_ x- (bu_ x+cu_ y)_ y+qu=f\quad in\quad \Omega,\quad u=0\quad on\quad \partial \Omega, \] where \(\Omega\) is a bounded rectangular region of \({\mathbb{R}}^ 2.\) The author extends some superconvergence results of the gradients of the solution at Gaussian points when the coefficients a, b and c are discontinuous along a piecewise straight line S in \(\Omega\). In this way, the author uses serendipity rectangular elements of degree 2 or 3.