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 Peclet number fixed, the estimates are suboptimal of order 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. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006

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