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.