The focus of this monograph is the development of space-time adaptive methods to solve the
convection reaction dominated non-stationary semi-linear advection diffusion reaction (ADR)
equations with internal boundary layers in an accurate and efficient way. After introducing the
ADR equations and discontinuous Galerkin discretization robust residual-based a posteriori
error estimators in space and time are derived. The elliptic reconstruction technique is then
utilized to derive the a posteriori error bounds for the fully discrete system and to obtain
optimal orders of convergence.As coupled surface and subsurface flow over large space and time
scales is described by (ADR) equation the methods described in this book are of high importance
in many areas of Geosciences including oil and gas recovery groundwater contamination and
sustainable use of groundwater resources storing greenhouse gases or radioactive waste in the
subsurface.
