An Inexpensive Method for the Evaluation of the Solution of the Lowest Order Raviart–Thomas Mixed Method

For the model problem - div(a∇ u) = f, we show how the approximate solution produced by the Raviart–Thomas [Lecture Notes in Mathematics 606, Springer-Verlag, Berlin, 1977] mixed method (of lowest degree) can be obtained from the solution of the P₁ nonconforming Galerkin method modified in a virtually cost-free manner.