FV Upwind Stabilization of FE Discretizations for Advection–Diffusion Problems
We apply a novel upwind stabilization of a mixed hybrid finite element method of lowest order to advection–diffusion problems with dominant advection and compare it with a finite element scheme stabilized by finite volume upwinding. Both schemes are locally mass conservative and employ an upwind-weighting formula in the discretization of the advective term. Numerical experiments indicate that the upwind-mixed method is competitive with the finite volume method. It prevents the appearance of spurious oscillations and produces nonnegative solutions for strongly advection-dominated problems, while the amount of artificial diffusion is lower than that of the finite volume method. This makes the method attractive for applications in which too much numerical diffusion is critical and may lead to false predictions; e.g., if highly nonlinear reactive processes take place only in thin interaction regions.
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