An Improved Optimal Order Mixed Finite Element Method for Semilinear Transport Problems - Bause, Markus; Brunner, Fabian; Knabner, Peter; Radu, Adrian Florin (Numerical Mathematics and Advanced Applications 2011, 2012)
We propose and study the numerical approximation of an advection-diffusion-reaction model equation by a modified Brezzi–Douglas–Marini mixed finite element method.Nonlinear advection is admitted, arising in complex and coupled flow and transport systems.In contrast to the classical variant of this approach, optimal second-order convergence of the scalar and the vector variable is ensured.No loss of rate of convergence due to the presence of the advection term is observe