Nonconforming finite element methods with subgrid viscosity applied to advection-diffusion-reaction equations

A nonconforming (Crouzeix-Raviart) finite element method with subgrid viscosity is analyzed to approximate advection-diffusion-reaction equations. The error estimates are quasi-optimal in the sense that keeping the Péclet number fixed, the estimates are suboptimal of order 1/2 in the mesh size for the L²-norm and optimal for the advective derivative on quasi-uniform meshes. The method is also reformulated as a finite volume box scheme providing a reconstruction formula for the diffusive flux with local conservation properties. Numerical results are presented to illustrate the error analysis.