Resumen
We consider a nonconforming streamline diffusion finite element method for solving convection-diffusion problems. The loss of the Galerkin orthogonality of the streamline diffusion method when applied to nonconforming finite element approximations results in an additional error term which cannot be estimated uniformly with respect to the perturbation parameter for the standard piecewise linear or rotated bilinear elements. Therefore, starting from the Crouzeix--Raviart element, we construct a modified nonconforming first order finite element space on shape regular triangular meshes satisfying a patch test of higher order. A rigorous error analysis of this P1mod element applied to a streamline diffusion discretization is given. The numerical tests show the robustness and the high accuracy of the new method.