Abstract
This chapter illustrates the numerical approximation of the weak formulations of an advection–diffusion–reaction boundary value problem using the Galerkin Finite Element Method (GFEM). In the first part of the chapter, the GFEM is applied to numerically discretize the displacement-based weak formulation, and then it is applied to the mixed weak formulation. The two approaches are compared and then the mixed method is adopted for the numerical study of the advection–diffusion–reaction boundary value problem. Stabilization techniques are introduced and analyzed to treat the case where the reaction and/or the advection terms are dominating over the diffusive term. The convergence of the GFEM is discussed and several numerical examples are illustrated to validate the theoretical predictions.
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