Higher order regularity and approximation of solutions to the Monod biodegradation model Original Research Article

In this work we continue analyzing mathematically the Monod model for biochemically reacting contaminant transport in the subsurface with regard to higher order regularity of solutions as well as further establishing a higher order approximation scheme in terms of an a priori error analysis relying on the regularity results. Recently, the existence and uniqueness of nonnegative global strong solutions to the Monod model was proved by Merz in [Adv. Math. Sci. (2005), in press]. The approximation scheme, based on higher order finite element methods and backward differentiation formulae, was suggested and analyzed numerically by Bause in [Comput. Visual. Sci 7 (2004) 61; M. Feistauer et al. (Eds.), Numerical Mathematics and Advanced Applications, ENUMATH 2003, Springer, 2004, pp. 112–122]. It was successfully applied to test problems of the literature (cf. [Internat. J. Numer. Methods Fluids 40 (2002) 79; IMA J. Numer. Anal. 22 (2002) 253]) as well as to complex scenarios with an additional calculation of the flow field by solving the parabolic-elliptic degenerate Richards equation; cf. [Comput. Visual. Sci. 7 (2004) 61]. The higher order approach has shown to reduce significantly the amount of inherent numerical diffusion compared to lower order ones. Thereby an artificial transverse mixing of the species leading to a strong overestimation of the biodegradation process and wrong prediction is avoided. To illustrate our approach, in this work the movement and expansion of a BTEX plume is studied for a “real world” field scale site.