Conforming and nonconforming finite element methods for solving the Darcy's equations

This paper deals with the finite element approximations of the solution of Darcy's equations. Both conforming and nonconforming finite element methods are studied, leading to optimal a priori estimates. However, because of the high order of the methods, the incompressibility condition is not exactly satisfied, which complicates the estimates of residual type errors indicators, introduced in view of mesh adaptivity.