## A Petrov-Galerkin formulation for advection-reaction-diffusion problems.(English)Zbl 0896.76042

We present a method called $$(\text{SU}+\text{C})\text{PG}$$ to solve advection-reaction-diffusion scalar equations by the finite element method. The SUPG (streamline upwind Petrov-Galerkin) extension is performed, covering the whole plane represented by the Péclet number and the dimensionless reaction number. The scheme is based on the extension of the super-convergence feature through the inclusion of an additional perturbation function and a corresponding proportionality constant. Both proportionality constants (the one corresponding to the standard perturbation function from SUPG, and the new one introduced here) are selected in order to verify the super-convergence. It is also shown that the $$(\text{SU}+\text{C})\text{PG}$$ scheme satisfies the discrete maximum principle, that guarantees uniform convergence of the finite element solution.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76R99 Diffusion and convection 76V05 Reaction effects in flows
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### References:

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