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Maximum norm error estimates for Div least-squares method for Darcy flows
Least-squares finite element methods for second order elliptic
partial differential equations such as Darcy flows are considered.
While there has been a significant progress in terms of obtaining
error estimates for the methods, the estimates are essentially based on
$L_2$-norm of the error. In this paper, we provide maximum norm error
estimates for the primary variable using a smoothed Green's function
introduced in 
and maximum norm error for the dual variables by taking advantage
of the fact that least-squares solutions are higher-order perturbations of
Galerkin solutions .